Решебник по алгебре 9 класс Мерзляк Задание 117

\[\boxed{\text{117\ (117).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ 6x > 18\]

\[x > 18\ :3\]

\[x > 3\]

\[Ответ:(3;\ + \infty).\]

\[2) - 2x \geq 10\]

\[x \leq 10\ :( - 2)\]

\[x \leq - 5\]

\[Ответ:( - \infty;\ - 5\rbrack.\]

\[3)\ \frac{1}{3}x < 9\]

\[x < 9 \cdot 3\]

\[x < 27\]

\[Ответ:( - \infty;27).\]

\[4)\ 0,1x \geq 0\]

\[x \geq 0\]

\[Ответ:\lbrack 0;\ + \infty).\]

\[5)\ \frac{3}{4}x > 24\]

\[x > 24 \cdot \frac{4}{3}\]

\[x > 32\]

\[Ответ:(32;\ + \infty)\]

\[6) - 10x < 0\]

\[x > 0\]

\[Ответ:(0; + \infty).\]

\[7)\ 2\frac{1}{4}x \leq - 1\frac{4}{5}\]

\[\frac{9}{4}x \leq - \frac{9}{5}\]

\[x \leq - \frac{9}{5} \cdot \frac{4}{9}\]

\[x \leq - \frac{4}{5}\]

\[Ответ:( - \infty;\ - 0,8\rbrack.\]

\[8) - 7x > \frac{14}{15}\]

\[x < \frac{14}{15} \cdot \left( - \frac{1}{7} \right)\]

\[x < - \frac{2}{15}\]

\[Ответ:\left( - \infty;\ - \frac{2}{15} \right).\]

\[9)\ 7x - 2 > 19\]

\[7x > 21\]

\[x > 3\]

\[Ответ:(3;\ + \infty).\]

\[10)\ 5x + 16 \leq 6\]

\[5x \leq - 10\]

\[x \leq - 2\]

\[Ответ:( - \infty;\ - 2\rbrack.\]

\[11)\ 4 - x < 5\]

\[- x < 1\]

\[x > - 1\]

\[Ответ:( - 1;\ + \infty).\]

\[12)\ 5 - 8x \geq 6\]

\[- 8x \geq 1\]

\[x \leq - \frac{1}{8}\]

\[Ответ:\left( - \infty;\ - \frac{1}{8} \right\rbrack\text{.\ }\ \]

\[13)\ 12 + 4x \geq 6x\]

\[12 \geq 2x\]

\[x \leq 6\]

\[Ответ:( - \infty;6\rbrack.\]

\[14)\ 36 - 2x < 4x\]

\[36 < 6x\]

\[x > 6\]

\[Ответ:(6;\ + \infty)\text{.\ }\]

\[15)\ \frac{x + 2}{5} < 2\ \ | \cdot 5\]

\[x + 2 < 10\]

\[x < 8\]

\[Ответ:( - \infty;8).\]