{"draftJsState":{"blocks":[{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Приветствуем всех, кто готовится к ОГЭ! Сегодня мы разберем задание №15 — одно из самых сложных в экзамене, но абсолютно решаемых при правильном подходе. Это задание проверяет ваше умение работать с различными типами неравенств и системами. Давайте разберем все по полочкам.","type":"unstyled","key":"c752l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"5957r"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":29,"offset":0,"style":"BOLD"}],"text":"Типы неравенств в задании №15","type":"unstyled","key":"fva64"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"4kglv"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":40,"offset":3,"style":"BOLD"}],"text":"1. Системы линейных и квадратных неравенств","type":"unstyled","key":"681nv"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"et04l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Алгоритм решения:","type":"unstyled","key":"6a8ln"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"capee"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Решите каждое неравенство системы отдельно","type":"unstyled","key":"2f81l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Найдите пересечение решений всех неравенств","type":"unstyled","key":"4it47"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Изобразите решение на числовой прямой","type":"unstyled","key":"6ar6c"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"afm2l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Пример:","type":"unstyled","key":"7vdjf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"1kql"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ 2x - 3 > 5","type":"unstyled","key":"du795"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ x² - 4x + 3 ≤ 0","type":"unstyled","key":"dbcug"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"5ai78"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"91m3c"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3ibag"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. 2x - 3 > 5 → 2x > 8 → x > 4","type":"unstyled","key":"b12me"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. x² - 4x + 3 ≤ 0 → (x-1)(x-3) ≤ 0 → x ∈ [1; 3]","type":"unstyled","key":"a3r58"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Пересечение: ∅ (решений нет)","type":"unstyled","key":"815ih"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"cnbql"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":43,"offset":3,"style":"BOLD"}],"text":"2. Рациональные неравенства (метод интервалов)","type":"unstyled","key":"4pk6u"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3vs2d"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Особенности: Неравенства содержат дроби","type":"unstyled","key":"d06r1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"8hi64"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Алгоритм решения:","type":"unstyled","key":"c5k5l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"4ct6g"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Перенести все в левую часть","type":"unstyled","key":"con0u"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Привести к общему знаменателю","type":"unstyled","key":"emb6u"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Найти нули числителя и знаменателя","type":"unstyled","key":"43l6g"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Отметить их на числовой прямой (точки из знаменателя — выколотые)","type":"unstyled","key":"4p5af"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Определить знаки на интервалах","type":"unstyled","key":"bsbab"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"6. Выбрать нужные интервалы","type":"unstyled","key":"a6u54"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"cqjvf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Пример: (x-2)/(x+3) ≥ 0","type":"unstyled","key":"28aks"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3m8mp"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Нули: x = 2 (числитель), x = -3 (знаменатель, выколотая)","type":"unstyled","key":"diqu1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"brhaa"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Интервалы: (-∞; -3), (-3; 2], [2; +∞)","type":"unstyled","key":"4qola"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"cvrem"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: x ∈ (-∞; -3) ∪ [2; +∞)","type":"unstyled","key":"832uc"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"828b1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":21,"offset":3,"style":"BOLD"}],"text":"3. Неравенства с модулем","type":"unstyled","key":"8jdsn"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"bk20v"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Основные методы:","type":"unstyled","key":"71u54"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"7q7bj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Раскрытие модуля по определению","type":"unstyled","key":"54hd6"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Возведение в квадрат (если обе части неотрицательны)","type":"unstyled","key":"589fm"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Геометрическая интерпретация","type":"unstyled","key":"dt7ll"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"45bc9"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Пример: |2x - 3| < 5","type":"unstyled","key":"bic50"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"58boj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение: -5< 2x - 3 < 5 -2< 2x < 8 -1< x < 4","type":"unstyled","key":"6rnoh"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"32g40"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: x ∈ (-1; 4)","type":"unstyled","key":"8h9hh"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3a511"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":40,"offset":0,"style":"BOLD"}],"text":"Метод интервалов для рациональных дробей","type":"unstyled","key":"6a6uh"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"24is"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Пошаговая инструкция:","type":"unstyled","key":"3ntla"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"dc3tn"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Привести неравенство к виду P(x)/Q(x) ⋄ 0 (⋄ — знак сравнения)","type":"unstyled","key":"2ot9v"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Найти нули числителя и знаменателя","type":"unstyled","key":"6mr21"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Отметить на числовой прямой (нули знаменателя — выколотые)","type":"unstyled","key":"1fkto"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Определить знаки на интервалах","type":"unstyled","key":"c7ben"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Выбрать интервалы согласно знаку неравенства","type":"unstyled","key":"dg4du"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"d6vkr"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":31,"offset":0,"style":"BOLD"}],"text":"Раскрытие модуля по определению","type":"unstyled","key":"9sfrl"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"9fo63"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Определение: |a| = { a, если a ≥ 0; -a, если a < 0 }","type":"unstyled","key":"f9gh1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"fkojn"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Алгоритм:","type":"unstyled","key":"d1pc1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"90s4p"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Найти точки, где выражение под модулем равно нулю","type":"unstyled","key":"37iv8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Разбить числовую прямую на интервалы","type":"unstyled","key":"2ogv7"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. На каждом интервале раскрыть модуль с соответствующим знаком","type":"unstyled","key":"3il7g"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Решить полученные неравенства","type":"unstyled","key":"1k2v8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Объединить решения с учетом области раскрытия","type":"unstyled","key":"2juo0"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"4vpci"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":29,"offset":0,"style":"BOLD"}],"text":"Отбор решений и запись ответа","type":"unstyled","key":"f2dhu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"2ir7"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Важные правила:","type":"unstyled","key":"dddgk"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"19brl"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Для строгих неравенств (<, >) используйте круглые скобки","type":"unstyled","key":"936o6"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Для нестрогих неравенств (≤, ≥) используйте квадратные скобки","type":"unstyled","key":"7r9kt"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Бесконечность всегда с круглой скобкой","type":"unstyled","key":"6l261"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Множество решений системы — пересечение решений","type":"unstyled","key":"9rnaj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Множество решений совокупности — объединение решений","type":"unstyled","key":"b43ue"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"ar86"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":36,"offset":0,"style":"BOLD"}],"text":"Типичные ошибки: Будьте внимательны!","type":"unstyled","key":"1dhc3"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"aq1gh"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Неверное раскрытие модуля:","type":"unstyled","key":"npjt"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неправильное определение знака на интервалах","type":"unstyled","key":"as864"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Потеря решений при переходе между интервалами","type":"unstyled","key":"enrak"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Ошибки в методе интервалов:","type":"unstyled","key":"3fp68"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неучет выколотых точек (нули знаменателя)","type":"unstyled","key":"8479i"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неверное определение знаков на интервалах","type":"unstyled","key":"6bpqt"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Неверное пересечение решений в системах:","type":"unstyled","key":"bib7k"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Путаница с объединением и пересечением","type":"unstyled","key":"4nt8p"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неправильное изображение на числовой прямой","type":"unstyled","key":"b9ovq"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Арифметические ошибки:","type":"unstyled","key":"ddtmi"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неверное решение составных неравенств","type":"unstyled","key":"bpnar"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Ошибки в преобразованиях","type":"unstyled","key":"2jnve"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Невнимательность к области определения:","type":"unstyled","key":"8pphu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Неучет ограничений (знаменатель ≠ 0)","type":"unstyled","key":"d0a2k"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · Потеря решений при возведении в квадрат","type":"unstyled","key":"btorr"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"btfm7"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":33,"offset":0,"style":"BOLD"}],"text":"Практика: Разбор заданий типа №15","type":"unstyled","key":"bb90t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"6tafo"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":0,"style":"BOLD"}],"text":"Задание 1. Решите систему неравенств:","type":"unstyled","key":"a23ju"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"eo5qe"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ x² - 5x + 6 < 0","type":"unstyled","key":"96c77"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ 2x + 1 ≥ 0","type":"unstyled","key":"bji07"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"avgcd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"daglj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"9ndn1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. x² - 5x + 6 < 0 → (x-2)(x-3) < 0 → x ∈ (2; 3)","type":"unstyled","key":"d3ftv"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. 2x + 1 ≥ 0 → x ≥ -0.5","type":"unstyled","key":"d8jcn"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Пересечение: x ∈ (2; 3)","type":"unstyled","key":"bicgd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"e2ngj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: (2; 3)","type":"unstyled","key":"94elj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"9iitn"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":0,"style":"BOLD"}],"text":"Задание 2. Решите неравенство:","type":"unstyled","key":"cf9lf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3dbd0"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"(x² - 4)/(x - 1) ≥ 0","type":"unstyled","key":"fb1aa"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"cbggk"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"e4q93"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"cg25b"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Нули числителя: x = -2, x = 2","type":"unstyled","key":"aljs"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Нуль знаменателя: x = 1 (выколотая)","type":"unstyled","key":"2bbor"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Интервалы: (-∞; -2], [-2; 1), (1; 2], [2; +∞)","type":"unstyled","key":"cfot1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Расставляем знаки:","type":"unstyled","key":"1dbo1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · x < -2: (+)/(-) = (-) — не подходит","type":"unstyled","key":"612sl"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · -2 < x < 1: (-)/(-) = (+) — подходит","type":"unstyled","key":"6975a"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · 1 < x < 2: (-)/(+) = (-) — не подходит","type":"unstyled","key":"abuh5"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · x > 2: (+)/(+) = (+) — подходит","type":"unstyled","key":"2c2u9"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"3ighl"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: x ∈ [-2; 1) ∪ [2; +∞)","type":"unstyled","key":"fvfsf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"1rm5h"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":0,"style":"BOLD"}],"text":"Задание 3. Решите неравенство:","type":"unstyled","key":"7vket"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"ahh3p"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"|2x - 1| > |x + 3|","type":"unstyled","key":"3177l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"c2gsu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"7el8r"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"6e0pg"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Возводим в квадрат обе части: (2x- 1)² > (x + 3)² 4x²- 4x + 1 > x² + 6x + 9 3x²- 10x - 8 > 0","type":"unstyled","key":"5u80g"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Решаем квадратное неравенство: D= 100 + 96 = 196 x= (10 ± 14)/6 x₁= 4, x₂ = -2/3","type":"unstyled","key":"fsr41"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Решение: x ∈ (-∞; -2/3) ∪ (4; +∞)","type":"unstyled","key":"c01t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"4d69r"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: x ∈ (-∞; -2/3) ∪ (4; +∞)","type":"unstyled","key":"as16t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"fic3o"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":0,"style":"BOLD"}],"text":"Задание 4. Решите систему:","type":"unstyled","key":"1v286"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"4aqrl"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ |x - 2| ≤ 3","type":"unstyled","key":"b4udd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"{ x² - 3x - 4 > 0","type":"unstyled","key":"3p3ch"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"8q724"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"ejvqm"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"94q8h"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. |x - 2| ≤ 3 → -3 ≤ x - 2 ≤ 3 → -1 ≤ x ≤ 5","type":"unstyled","key":"1p2qu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. x² - 3x - 4 > 0 → (x-4)(x+1) > 0 → x ∈ (-∞; -1) ∪ (4; +∞)","type":"unstyled","key":"5ujj3"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Пересечение: x ∈ [-1; 5] ∩ [(-∞; -1) ∪ (4; +∞)] = (4; 5]","type":"unstyled","key":"fe11p"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"1fddj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: (4; 5]","type":"unstyled","key":"b2u66"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"f29aq"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":0,"style":"BOLD"}],"text":"Задание 5. Решите неравенство:","type":"unstyled","key":"5fdkg"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"clefc"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"(x + 1)²(x - 3)/(x - 2) ≤ 0","type":"unstyled","key":"brle6"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"67n8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Решение:","type":"unstyled","key":"ac1mi"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"2np9n"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Нули: x = -1 (кратность 2), x = 3","type":"unstyled","key":"b1scc"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Выколотая точка: x = 2","type":"unstyled","key":"6iq27"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Учитываем четность корня (x = -1) — знак не меняется","type":"unstyled","key":"4qqt3"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Интервалы: (-∞; -1], [-1; 2), (2; 3], [3; +∞)","type":"unstyled","key":"2pdi0"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Расставляем знаки:","type":"unstyled","key":"71fgu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · x < -1: (+)*(-)/(-) = (+) — не подходит","type":"unstyled","key":"dhcfp"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · -1 < x < 2: (+)*(-)/(-) = (+) — не подходит","type":"unstyled","key":"5lid1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · 2 < x < 3: (+)*(-)/(+) = (-) — подходит","type":"unstyled","key":"2hpgp"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":" · x > 3: (+)*(+)/(+) = (+) — не подходит","type":"unstyled","key":"96v97"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"b1utu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Ответ: x ∈ (2; 3]","type":"unstyled","key":"njka"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"b4dag"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":39,"offset":0,"style":"BOLD"}],"text":"Полезные советы для решения задания №15","type":"unstyled","key":"5iddj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"jd7t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"1. Внимательно читайте условие — определите тип неравенства","type":"unstyled","key":"7jnm"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"2. Действуйте поэтапно — не пытайтесь решить все сразу","type":"unstyled","key":"3unbs"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"3. Всегда проверяйте полученные решения","type":"unstyled","key":"8pdnr"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"4. Используйте числовую прямую для наглядности","type":"unstyled","key":"1od5b"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"5. Помните об области определения — исключайте точки, где выражение не имеет смысла","type":"unstyled","key":"17m09"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"6. Тренируйтесь на задачах разного уровня сложности","type":"unstyled","key":"433ta"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"bbte9"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"9nols"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Задание №15 требует системного подхода и внимательности. Ключ к успеху — понимание методов решения каждого типа неравенств и умение избегать типичных ошибок.","type":"unstyled","key":"27n6s"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"a9ua8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":17,"offset":0,"style":"BOLD"}],"text":"Основные моменты:","type":"unstyled","key":"9froi"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"bm31t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Для систем находите пересечение решений","type":"unstyled","key":"1k46u"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Для дробно-рациональных неравенств используйте метод интервалов","type":"unstyled","key":"csr0c"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Для модулей аккуратно раскрывайте знаки","type":"unstyled","key":"8ld4e"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"· Всегда проверяйте область определения","type":"unstyled","key":"9o73j"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"unstyled","key":"325c2"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Регулярная практика решения задач разного типа поможет вам уверенно справиться с заданием №15 на ОГЭ. Удачи в подготовке!","type":"unstyled","key":"2gspd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"marker","key":"jwlmXyJ5Jesj9cqvdloi"}],"entityMap":{}},"mentions":[]}