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Здравствуйте, Лилия! Я, например, могу решить указанное Вами уравнение, но не понимаю, что значит "правильно записать ход решения". Сообщите, пожалуйста, что Вы имеете в виду.
Обозначение модуля убирается в каждом из промежутков, на которые числовая прямая разбивается граничными точками. Если в условии присутствует двойной модуль (модуль в выражении под знаком модуля), то сначала лучше снять знак внутреннего модуля, а потом, сохраняя уже полученные граничные точки, заняться снятием внешнего модуля.
Обозначение модуля убирается в каждом из промежутков, на которые числовая прямая разбивается граничными точками. Если в условии присутствует двойной модуль (модуль в выражении под знаком модуля), то сначала лучше снять знак внутреннего модуля, а потом, сохраняя уже полученные граничные точки, заняться снятием внешнего модуля.
Здравствуйте, Лилия! Чтобы не запутаться с разбиением на всевозможные интервалы, лучше поступить так. Заметим, что модуль в правой части убирается сразу, т.к. при 6-x < 0 решений нет (проверьте). После этого уравнение приводится к виду ||2x-1| - 5| = -(2x - 1) + 5. Делаем подстановку y = 2x - 1, получим ||y| - 5| = -y + 5. Придется рассмотреть три интервала y< -5, -5 <= y < 0, 0 <= y <= 5. В первых двух нет решений, в последнем y - любое. То есть, x - любое число в интервале [1/2, 3]. (Не только x = 3).
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Лилия