Решебник по алгебре 7 класс Мерзляк ФГОС Задание 68

 

\[\boxed{\text{68\ (68).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

\[x + 3x = 12\]

\[4x = 2\]

\[x = 3.\]

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

\[- x + 3x = 12\]

\[2x = 12\]

\[x = 6 - не\ удовлетворяет.\]

\[Ответ:x = 3.\]

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

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

\[x - 4x = 9\]

\(- 3x = 9\)

\[x = - 3 - не\ удовлетворяет.\]

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

\[- x - 4x = 9\]

\[- 5x = 9\]

\[x = - 1,8.\]

\[Ответ:\ x = - 1,8.\]

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

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

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

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

\[- 4x = - 8\]

\[x = 2.\]

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

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

\[8x = - 18 + 10\]

\[8x = - 8\]

\[x = - 1.\]

\[Ответ:\ x = - 1;2.\]

\[\boxed{\text{68.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1 - весь\ огород.\]

\[1)\ 1 - \frac{5}{18} = \frac{13}{18}\ (часть) -\]

\[пропололи\ Василий\ и\ Федор.\]

\[2)\ \frac{13}{18} \cdot \frac{6}{13} = \frac{6}{18} = \frac{1}{3}\ (часть) -\]

\[прополол\ Василий.\]

\[3)\ 1 - \left( \frac{5}{18} + \frac{1^{\backslash 6}}{3} \right) = 1 - \frac{5 + 6}{18} =\]

\[= 1 - \frac{11}{18} = \frac{7}{18}\ (часть) -\]

\[прополол\ Федор.\]

\[4)\ Сравним:\]

\[\frac{5}{18} < \frac{6}{18} < \frac{7}{18}.\]

\[Наибольшую\ часть\ прополол\ \]

\[Федор.\]

\[Ответ:Федор.\ \]