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Консультация № 190483
26.01.2017, 12:01
0.00 руб.
0
9
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Решить неравенство 1/х<1.
Варианты ответов:
1) х>1
2) х ∈ (-∞; 0) U (1;+ ∞)
3) х<0.
Решить неравенство 1/х<1.
Варианты ответов:
1) х>1
2) х ∈ (-∞; 0) U (1;+ ∞)
3) х<0.
Обсуждение
26.01.2017, 12:10
общий
это ответ
Здравствуйте, svrvsvrv!
Решением является
Решением является
5
Спасибо
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.01.2017, 12:36
общий
Как из Вашего решения понять, что ответ именно такой, как Вы предложили?
А такое решение неправильно:
1/х<1
1/х * х < 1*х
1<х²
1<х
х>1 ?
А такое решение неправильно:
1/х<1
1/х * х < 1*х
1<х²
1<х
х>1 ?
26.01.2017, 12:41
общий
26.01.2017, 12:42
Адресаты:
Понять можно, если применить метод интервалов, например. Непосредственно проверить можно подстановкой значений из интервалов. А Ваше решение неверное, потому что знак получающегося неравенства зависит от знака числа 
Кроме того, Вы допустили ошибки при умножении.
Кроме того, Вы допустили ошибки при умножении.
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.01.2017, 12:45
общий
Простите, ошибка в умножении от того, что я не поставила скобки. Надо было:
1/х<1
(1/х) * х < 1*х
1<х²
1<х
х>1
1/х<1
(1/х) * х < 1*х
1<х²
1<х
х>1
26.01.2017, 12:48
общий
svrvsvrv Простите, ошибка в умножении от того, что я не поставила скобки. Надо было:
1/х<1
(1/х) * х < 1*х
1<х²
1<х
х>1
Как Вы получили
?
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.01.2017, 12:57
общий
Ошибка. Для того, чтобы избавиться от х в знаменателе, правая и левая часть неравенства умножались на х (дальше - ошибка в вычислении: надо не х², а х). Тогда получается:
1/х<1
(1/х) * х < 1*х
1<х
х>1
1/х<1
(1/х) * х < 1*х
1<х
х>1
26.01.2017, 13:08
общий
Адресаты:
Да, получается 
если обе части исходного неравенства умножить на число 
Теперь рассмотрите, что получится, если обе части исходного неравенства умножить на число 
если обе части исходного неравенства умножить на число Теперь рассмотрите, что получится, если обе части исходного неравенства умножить на число
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.01.2017, 13:16
общий
Адресаты:
Чтобы проверить себя, можно еще нарисовать график гиперболы 1/х и посмотреть, когда ордината y меньше 1
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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