Предмет: Математика, автор: karolprismont

Решите неравенство 2x(0,5x-2)≤0

Ответы

Автор ответа: etoa872

ДЕЙСТВИЯ ПО РЕШЕНИЮ

2x(0.5x−2)≤0

Чтобы умножить 2x на 0.5x−2, используйте свойство дистрибутивности.

−4x≤0

Вынесите x за скобки.

x(x−4)≤0

Чтобы получить произведение ≤0, одно из значений x и x−4 должно быть ≥0, а другое — ≤0. Consider the case when x≥0 and x−4≤0.

x≥0

x−4≤0

Решение, которое удовлетворяет обоим неравенствам: x∈[0,4].

x∈[ 0,4 ]

Consider the case when x≤0 and x−4≥0.

x−4≥0

x≤0

Это неверно для любого x.

x∈∅

Окончательное решение — это объединение полученных решений.

x∈[ 0,4 ]

etoa872: понятно?

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