Решебник по алгебре 7 класс Мерзляк ФГОС Задание 141

 

\[\boxed{\text{141\ (141).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ a + ( - a) = 0 -\]

\[тождество \Longrightarrow \ \ 0 = 0.\]

\[2)\ a \cdot 1 = 1 - не\ тождество \Longrightarrow\]

\[\Longrightarrow так\ как\ при\ a \neq 1\ будет\ \]

\[неверным.\]

\[3)\ a \cdot ( - 1) = - a -\]

\[тождество \Longrightarrow - a = - a.\]

\[4)\ |a| = | - a| - тождество \Longrightarrow \text{\ \ \ }\]

\[\Longrightarrow \text{\ \ \ }a = a.\]

\[5)\ a - ( - a) = 0 -\]

\[не\ тождество \Longrightarrow \ \ a + a \neq 0.\ \]

\[\boxed{\text{141.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ |x| + 3x = 12\]

\[x \geq 0;\ \ |x| = x:\]

\[x + 3x = 12\]

\[4x = 2\]

\[x = 3.\]

\[x < 0;\ \ |x| = - x:\]

\[- x + 3x = 12\]

\[2x = 12\]

\[x = 6 - не\ удовлетворяет.\]

\[Ответ:x = 3.\]

\[2)\ |x| - 4x = 9\]

\[x \geq 0;\ \ |x| = x:\]

\[x - 4x = 9\]

\(- 3x = 9\)

\[x = - 3 - не\ удовлетворяет.\]

\[x < 0;\ \ \ |x| = - x:\]

\[- x - 4x = 9\]

\[- 5x = 9\]

\[x = - 1,8.\]

\[Ответ:\ x = - 1,8.\]

\[3)\ 2 \cdot (x - 5) - 6 \cdot |x| = - 18\]

\[x \geq 0;\ \ |x| = x:\]

\[2x - 10 - 6x = - 18\]

\[- 4x = - 18 + 10\]

\[- 4x = - 8\]

\[x = 2.\]

\[x < 0;\ \ |x| = - x:\]

\[2x - 10 + 6x = - 18\]

\[8x = - 18 + 10\]

\[8x = - 8\]

\[x = - 1.\]

\[Ответ:\ x = - 1;2.\]