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Номер 8, страница 44 - гдз по алгебре 9 класс учебник Бунимович, Кузнецова
Авторы: Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О., Суворова С. Б.
Тип: Учебник
Серия: сферы 1-11
Издательство: Просвещение
Год издания: 2018 - 2026
Цвет обложки: оранжевый с диаграммой
ISBN: 978-5-09-051312-8
Популярные ГДЗ в 9 классе
Глава 1. Неравенства. Подведём итоги - номер 8, страница 44.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198649 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Неравенства" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "7" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Book {#1057 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2789 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:5 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1079 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1081 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Term {#1082 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Term {#1075 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы 1-11" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery 1-11" ] #original: array:8 [ "id" => 4796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы 1-11" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery 1-11" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с диаграммой" 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#items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Term {#1089 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => array:6 [ …6] "field_translit" => "oranzhevyy" ] #original: array:6 [ "id" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => array:6 [ …6] "field_translit" => "oranzhevyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] 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Алгебраические выражения порой способны поставить в тупик и отличников, что уж говорить о подростках, которые больше склонны к гуманитарным дисциплинам? Поэтому помощь <strong>ГДЗ по алгебре 9 класс учебное пособие Бунимович, Кузнецова, Минаева (Просвещение)</strong> может оказаться незаменимой, особенно при текущих нагрузках. </p> <p> Больше всего трудностей возникает у ребят при изучении следующих тем: </p> <ol> <li>Общие свойства неравенств.</li> <li>Квадратичная функция и её график.</li> <li>Рациональные выражения.</li> <li>Числовые последовательности.</li> <li>Интервальный ряд. Гистограмма.</li> <li>Статистическое оценивание и прогноз.</li> </ol> <p> Уроки нередко проходят срезано, так как за 45 минут преподавателям нужно многое успеть. Они объясняют лишь часть темы, оставляя все остальное для самостоятельного разбора. Но много ли учеников проводит дома свободное время с учебником? Конечно, нет. В основном учащиеся наспех выполняют заданные номера и моментально забывают о них. 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Поэтому большинство школьников подходит к работе с <strong>решебником Бунимовича по алгебре за 9 класс</strong> ответственно и внимательно. </p> <p> Учителя-предметники, да и сами авторы пособия рекомендуют всегда придерживаться следующих правил: </p> <ol> <li>не забывать про освоение теоретического материала;</li> <li>выполнять домашние задания без подсказок со стороны;</li> <li>когда все сделано, можно приступать к сверке решений по ГДЗ;</li> <li>работа над ошибками - тоже немаловажный аспект.</li> </ol> <p> Подобный подход несомненно принесет пользу, а результаты станут заметны через пару занятий. Первая же контрольная принесет хорошие плоды, так как перед этим подростки подробно проработали все аспекты каждого параграфа. Происходит это ненавязчиво и не отнимает много времени, что придется по душе всем ребятам. </p> <h2> Чем именно полезен решебник? </h2> <p> Современная учебная программа в основном направлена на практику. Считается, что чем больше упражнений выполнят школьники, тем лучше они поймут новую тему. Но не всегда такой метод срабатывает. Все же понимание теории - немаловажная составляющая полноценных знаний по предмету. Но в условиях тотальных нагрузок преподавателям просто не остается достаточно времени для проработки всех нюансов. Так что у ребят остается один шанс не упустить ничего важного - это использовать <strong>гдз по алгебре 9 класс к учебнику Бунимович Е.А (2018-2023 гг.)</strong>. </p> <p> Для того чтобы упростить ученикам понимание параграфов, авторы издания разместили в нем: </p> <ul> <li>подробные решения ко всем номерам;</li> <li>верные ответы;</li> <li>готовые графики и заполненные таблицы;</li> <li>детальные наглядные примеры.</li> </ul> <p> Все, что нужно сделать подросткам - это правильно воспользоваться предоставленными сведениями. Расположение решебника и постоянный онлайн-доступ делают работу с ним простым делом, которое займет от силы несколько минут. 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"field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 198659 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Подведём итоги" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "43" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:3 [ 0 => App\Models\Element {#1098 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 211138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1099 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 700 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_content_source" => null ] #original: array:21 [ "id" => 700 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "198830" "type" => "task" ] "text" => "<p><strong>8</strong> Решите неравенство и изобразите множество его решений на координатной прямой:</p><p><strong>а)</strong> $1 - 5x > -4;$</p><p><strong>б)</strong> $4 - 3x \le x + 16;$</p><p><strong>в)</strong> $2x - 5(x - 3) < 16 - 6x;$</p><p><strong>г)</strong> $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-itog-43/8-1.webp?ts=1734190529" ] ] ] #original: array:7 [ "id" => 211138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "198830" "type" => "task" ] "text" => "<p><strong>8</strong> Решите неравенство и изобразите множество его решений на координатной прямой:</p><p><strong>а)</strong> $1 - 5x > -4;$</p><p><strong>б)</strong> $4 - 3x \le x + 16;$</p><p><strong>в)</strong> $2x - 5(x - 3) < 16 - 6x;$</p><p><strong>г)</strong> $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-itog-43/8-1.webp?ts=1734190529" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1093 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 212251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Edition {#1090 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_content_source" => null ] #original: array:21 [ "id" => 701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "198830" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/1-itog-43/8-1.webp?ts=1734190579" ] ] ] #original: array:6 [ "id" => 212251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034} "task" => array:2 [ "refs" => "198830" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/1-itog-43/8-1.webp?ts=1734190579" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1043 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1421797 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Edition {#1041 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "198830" "type" => "task" ] "text" => "<p><strong>а)</strong> $1 - 5x > -4$</p><p><span>Перенесем 1 в правую часть неравенства, изменив знак:</span></p><p>$-5x > -4 - 1$</p><p>$-5x > -5$</p><p><span>Разделим обе части неравенства на -5. При делении на отрицательное число знак неравенства меняется на противоположный:</span></p><p>$x < \frac{-5}{-5}$</p><p>$x < 1$</p><p><span>Множество решений в виде интервала: $(-\infty; 1)$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка 1 "выколота", так как неравенство строгое.</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="white"></circle> <text x="145" y="75" font-family="Arial" font-size="16">1</text></svg><p><span>Ответ: $x \in (-\infty; 1)$.</span></p><p><strong>б)</strong> $4 - 3x \le x + 16$</p><p><span>Сгруппируем слагаемые с переменной $x$ в левой части, а свободные члены — в правой:</span></p><p>$-3x - x \le 16 - 4$</p><p>$-4x \le 12$</p><p><span>Разделим обе части неравенства на -4, изменив знак неравенства на противоположный:</span></p><p>$x \ge \frac{12}{-4}$</p><p>$x \ge -3$</p><p><span>Множество решений в виде интервала: $[-3; +\infty)$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка -3 "закрашена", так как неравенство нестрогое.</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="150" y1="50" x2="290" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="#007bff"></circle> <text x="140" y="75" font-family="Arial" font-size="16">-3</text></svg><p><span>Ответ: $x \in [-3; +\infty)$.</span></p><p><strong>в)</strong> $2x - 5(x - 3) < 16 - 6x$</p><p><span>Раскроем скобки в левой части неравенства:</span></p><p>$2x - 5x + 15 < 16 - 6x$</p><p><span>Приведем подобные слагаемые в левой части:</span></p><p>$-3x + 15 < 16 - 6x$</p><p><span>Перенесем слагаемые с $x$ в левую часть, а свободные члены — в правую:</span></p><p>$-3x + 6x < 16 - 15$</p><p>$3x < 1$</p><p><span>Разделим обе части на 3:</span></p><p>$x < \frac{1}{3}$</p><p><span>Множество решений в виде интервала: $(-\infty; \frac{1}{3})$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка $\frac{1}{3}$ "выколота".</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="white"></circle> <text x="140" y="75" font-family="Arial" font-size="16">1/3</text></svg><p><span>Ответ: $x \in (-\infty; \frac{1}{3})$.</span></p><p><strong>г)</strong> $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1$</p><p><span>Чтобы избавиться от дробей, умножим обе части неравенства на наименьший общий знаменатель, который равен $НОК(7, 3) = 21$:</span></p><p>$21 \cdot \left(\frac{1 - x}{7} + \frac{2 - x}{3}\right) \ge 21 \cdot 1$</p><p>$3(1 - x) + 7(2 - x) \ge 21$</p><p><span>Раскроем скобки:</span></p><p>$3 - 3x + 14 - 7x \ge 21$</p><p><span>Приведем подобные слагаемые:</span></p><p>$17 - 10x \ge 21$</p><p><span>Перенесем 17 в правую часть:</span></p><p>$-10x \ge 21 - 17$</p><p>$-10x \ge 4$</p><p><span>Разделим обе части на -10, изменив знак неравенства на противоположный:</span></p><p>$x \le \frac{4}{-10}$</p><p>$x \le -\frac{2}{5}$</p><p><span>Множество решений в виде интервала: $(-\infty; -\frac{2}{5}]$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка $-\frac{2}{5}$ "закрашена".</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="#007bff"></circle> <text x="135" y="75" font-family="Arial" font-size="16">-2/5</text></svg><p><span>Ответ: $x \in (-\infty; -\frac{2}{5}]$.</span></p>" ] #original: array:6 [ "id" => 1421797 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119} "task" => array:2 [ "refs" => "198830" "type" => "task" ] "text" => "<p><strong>а)</strong> $1 - 5x > -4$</p><p><span>Перенесем 1 в правую часть неравенства, изменив знак:</span></p><p>$-5x > -4 - 1$</p><p>$-5x > -5$</p><p><span>Разделим обе части неравенства на -5. При делении на отрицательное число знак неравенства меняется на противоположный:</span></p><p>$x < \frac{-5}{-5}$</p><p>$x < 1$</p><p><span>Множество решений в виде интервала: $(-\infty; 1)$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка 1 "выколота", так как неравенство строгое.</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="white"></circle> <text x="145" y="75" font-family="Arial" font-size="16">1</text></svg><p><span>Ответ: $x \in (-\infty; 1)$.</span></p><p><strong>б)</strong> $4 - 3x \le x + 16$</p><p><span>Сгруппируем слагаемые с переменной $x$ в левой части, а свободные члены — в правой:</span></p><p>$-3x - x \le 16 - 4$</p><p>$-4x \le 12$</p><p><span>Разделим обе части неравенства на -4, изменив знак неравенства на противоположный:</span></p><p>$x \ge \frac{12}{-4}$</p><p>$x \ge -3$</p><p><span>Множество решений в виде интервала: $[-3; +\infty)$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка -3 "закрашена", так как неравенство нестрогое.</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="150" y1="50" x2="290" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="#007bff"></circle> <text x="140" y="75" font-family="Arial" font-size="16">-3</text></svg><p><span>Ответ: $x \in [-3; +\infty)$.</span></p><p><strong>в)</strong> $2x - 5(x - 3) < 16 - 6x$</p><p><span>Раскроем скобки в левой части неравенства:</span></p><p>$2x - 5x + 15 < 16 - 6x$</p><p><span>Приведем подобные слагаемые в левой части:</span></p><p>$-3x + 15 < 16 - 6x$</p><p><span>Перенесем слагаемые с $x$ в левую часть, а свободные члены — в правую:</span></p><p>$-3x + 6x < 16 - 15$</p><p>$3x < 1$</p><p><span>Разделим обе части на 3:</span></p><p>$x < \frac{1}{3}$</p><p><span>Множество решений в виде интервала: $(-\infty; \frac{1}{3})$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка $\frac{1}{3}$ "выколота".</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="white"></circle> <text x="140" y="75" font-family="Arial" font-size="16">1/3</text></svg><p><span>Ответ: $x \in (-\infty; \frac{1}{3})$.</span></p><p><strong>г)</strong> $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1$</p><p><span>Чтобы избавиться от дробей, умножим обе части неравенства на наименьший общий знаменатель, который равен $НОК(7, 3) = 21$:</span></p><p>$21 \cdot \left(\frac{1 - x}{7} + \frac{2 - x}{3}\right) \ge 21 \cdot 1$</p><p>$3(1 - x) + 7(2 - x) \ge 21$</p><p><span>Раскроем скобки:</span></p><p>$3 - 3x + 14 - 7x \ge 21$</p><p><span>Приведем подобные слагаемые:</span></p><p>$17 - 10x \ge 21$</p><p><span>Перенесем 17 в правую часть:</span></p><p>$-10x \ge 21 - 17$</p><p>$-10x \ge 4$</p><p><span>Разделим обе части на -10, изменив знак неравенства на противоположный:</span></p><p>$x \le \frac{4}{-10}$</p><p>$x \le -\frac{2}{5}$</p><p><span>Множество решений в виде интервала: $(-\infty; -\frac{2}{5}]$.</span></p><p><span>Изобразим множество решений на координатной прямой. Точка $-\frac{2}{5}$ "закрашена".</span></p><svg width="300" height="100" viewBox="0 0 300 100" xmlns="http://www.w3.org/2000/svg"> <line x1="10" y1="50" x2="290" y2="50" stroke="black" stroke-width="2"></line> <polygon points="290,50 280,45 280,55" fill="black"></polygon> <text x="285" y="70" font-family="Arial" font-size="16">x</text> <line x1="10" y1="50" x2="150" y2="50" stroke="#007bff" stroke-width="4"></line> <line x1="150" y1="45" x2="150" y2="55" stroke="black" stroke-width="2"></line> <circle cx="150" cy="50" r="4" stroke="#007bff" stroke-width="2" fill="#007bff"></circle> <text x="135" y="75" font-family="Arial" font-size="16">-2/5</text></svg><p><span>Ответ: $x \in (-\infty; -\frac{2}{5}]$.</span></p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "198831" "type" => "task" ] "previous" => array:2 [ "refs" => "198829" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1112 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 926390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_url" => "/9-klass/algebra/bunimovich-uchebnik/page-44" "field_display_title" => "44" "field_folder" => "1" "field_image_name" => "44" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1110 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Element {#1133 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1100487 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1135 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1100487 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1135 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "926391" "type" => "book_page" ] "previous" => array:2 [ "refs" => "926389" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:9 [ 0 => App\Models\Task {#1223 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1224 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1225 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1227 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1236 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1224 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1225 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1227 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1236 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1229 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1235 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1237 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233 …2} "content" => Illuminate\Database\Eloquent\Collection {#1231 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1235 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1237 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233 …2} "content" => Illuminate\Database\Eloquent\Collection {#1231 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1232 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198831 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1245 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1246 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1247 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198831 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1245 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1246 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1247 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1250 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1256 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1254 …2} "content" => Illuminate\Database\Eloquent\Collection {#1253 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1271 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1256 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1254 …2} "content" => Illuminate\Database\Eloquent\Collection {#1253 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1271 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1255 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1270 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1285 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1270 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1285 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1269 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1286 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 …2} "content" => Illuminate\Database\Eloquent\Collection {#1281 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1299 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1286 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 …2} "content" => Illuminate\Database\Eloquent\Collection {#1281 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1299 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1283 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198835 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" 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false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Task {#1297 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 198836 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "44" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/itog-43-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1312 …2} "top_parent_branch" => 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"book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№8 (с. 44)
Условие. №8 (с. 44)
скриншот условия
8 Решите неравенство и изобразите множество его решений на координатной прямой:
а) $1 - 5x > -4;$
б) $4 - 3x \le x + 16;$
в) $2x - 5(x - 3) < 16 - 6x;$
г) $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1.$
Решение. №8 (с. 44)
Решение 2. №8 (с. 44)
а) $1 - 5x > -4$
Перенесем 1 в правую часть неравенства, изменив знак:
$-5x > -4 - 1$
$-5x > -5$
Разделим обе части неравенства на -5. При делении на отрицательное число знак неравенства меняется на противоположный:
$x < \frac{-5}{-5}$
$x < 1$
Множество решений в виде интервала: $(-\infty; 1)$.
Изобразим множество решений на координатной прямой. Точка 1 "выколота", так как неравенство строгое.
Ответ: $x \in (-\infty; 1)$.
б) $4 - 3x \le x + 16$
Сгруппируем слагаемые с переменной $x$ в левой части, а свободные члены — в правой:
$-3x - x \le 16 - 4$
$-4x \le 12$
Разделим обе части неравенства на -4, изменив знак неравенства на противоположный:
$x \ge \frac{12}{-4}$
$x \ge -3$
Множество решений в виде интервала: $[-3; +\infty)$.
Изобразим множество решений на координатной прямой. Точка -3 "закрашена", так как неравенство нестрогое.
Ответ: $x \in [-3; +\infty)$.
в) $2x - 5(x - 3) < 16 - 6x$
Раскроем скобки в левой части неравенства:
$2x - 5x + 15 < 16 - 6x$
Приведем подобные слагаемые в левой части:
$-3x + 15 < 16 - 6x$
Перенесем слагаемые с $x$ в левую часть, а свободные члены — в правую:
$-3x + 6x < 16 - 15$
$3x < 1$
Разделим обе части на 3:
$x < \frac{1}{3}$
Множество решений в виде интервала: $(-\infty; \frac{1}{3})$.
Изобразим множество решений на координатной прямой. Точка $\frac{1}{3}$ "выколота".
Ответ: $x \in (-\infty; \frac{1}{3})$.
г) $\frac{1 - x}{7} + \frac{2 - x}{3} \ge 1$
Чтобы избавиться от дробей, умножим обе части неравенства на наименьший общий знаменатель, который равен $НОК(7, 3) = 21$:
$21 \cdot \left(\frac{1 - x}{7} + \frac{2 - x}{3}\right) \ge 21 \cdot 1$
$3(1 - x) + 7(2 - x) \ge 21$
Раскроем скобки:
$3 - 3x + 14 - 7x \ge 21$
Приведем подобные слагаемые:
$17 - 10x \ge 21$
Перенесем 17 в правую часть:
$-10x \ge 21 - 17$
$-10x \ge 4$
Разделим обе части на -10, изменив знак неравенства на противоположный:
$x \le \frac{4}{-10}$
$x \le -\frac{2}{5}$
Множество решений в виде интервала: $(-\infty; -\frac{2}{5}]$.
Изобразим множество решений на координатной прямой. Точка $-\frac{2}{5}$ "закрашена".
Ответ: $x \in (-\infty; -\frac{2}{5}]$.
Другие задания:
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