Решебник по алгебре 8 класс Мерзляк ФГОС Задание 992

\[\boxed{\mathbf{992.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 3 - 5(2x + 4) \geq 7 - 2x\]

\[3 - 10x - 20 \geq 7 - 2x\]

\[- 10x + 2x \geq 7 - 3 + 20\]

\[- 8x \geq 24\]

\[x \leq - 3\]

\[Ответ:x \in ( - \infty;\ - 3\rbrack.\]

\[2)\ 6x - 3(x - 1) \leq 2 + 5x\]

\[6x - 3x + 3 - 2 - 5x \leq 0\]

\[- 2x \leq - 1\]

\[x \geq 0,5\]

\[Ответ:x \in \lbrack 0,5;\ + \infty).\]

\[3)\ x - 2(x - 1) \geq 10 + 3(x + 4)\]

\[x - 2x + 2 \geq 10 + 3x + 12\]

\[x - 2x - 3x \geq 22 - 2\]

\[- 4x \geq 20\]

\[x \leq - 5\]

\[Ответ:x \in ( - \infty;\ - 5\rbrack.\]

\[4)\ 2(2x - 3,5) -\]

\[- 3(2 - 3x) < 6(1 - x)\]

\[4x - 7 - 6 + 9x < 6 - 6x\]

\[4x + 9x + 6x < 6 + 7 + 6\]

\[19x < 19\]

\[x < 1\]

\[Ответ:x \in ( - \infty;1).\]

\[5)\ (x + 1)(x - 2)\ \leq\]

\[\leq (x - 3)(x + 3)\]

\[x^{2} - 2x + x - 2 \leq x^{2} + 3x -\]

\[- 3x - 9\]

\[x^{2} - 2x + x - x^{2} -\]

\[- 3x + 3x \leq - 9 + 2\]

\[- x \leq - 7\]

\[x \geq 7\]

\[Ответ:x \in \lbrack 7;\ + \infty).\]

\[6)\ \frac{3x + 7}{4} - \frac{5x - 2}{2} < x\]

\[\frac{3x + 7 - 10x + 4}{4} < x\ \ | \cdot 4\]

\[- 7x + 11 < 4x\]

\[- 11x < - 11\]

\[x > 1\]

\[Ответ:x \in (1;\ + \infty).\]

\[7)\ (x - 5)(x + 1) \leq 3 + (x - 2)^{2}\]

\[x^{2} + x - 5x - 5 \leq 3 + x^{2} -\]

\[- 4x + 4\]

\[x^{2} - x^{2} + x - 5x + 4x \leq 3 +\]

\[+ 4 + 5\]

\[0 \leq 12\]

\[Ответ:x \in ( - \infty; + \infty).\]

\[8)\ \frac{x + 1}{2} - \frac{x - 3}{3} > 2 + \frac{x}{6}\]

\[\frac{3x + 3 - 2x + 6}{6} > \frac{12 + x}{6}\ \ \ | \cdot 6\]

\[3x + 3 - 2x + 6 > 12 + x\]

\[x + 9 > 12 + x\]

\[9 > 12 - неверно.\]

\[Ответ:\ \varnothing.\]