Решебник по алгебре 9 класс Мерзляк Задание 204

\[\boxed{\text{204\ (204).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (14 - 7x)(x + 3) > 0\]

\[14 - 7x = 0\ \ \ или\ \ \ x + 3 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 3\]

\(\ \)

\[Ответ:x \in ( - 3;2).\]

\[2)\ \frac{x - 8}{3x - 12} > 0\ \ \ | \cdot (3x - 12)\]

\[(x - 8)(3x - 12) > 0,\ \ \]

\[3x - 12 \neq 0,\ \ x \neq 4\]

\[x - 8 = 0\]

\[x = 8\]

\(\ \)

\[Ответ:x \in ( - \infty;4) \cup (8;\ + \infty).\]

\[3)\ \frac{5x - 6}{x + 9} \geq 0\ \ \ \ \ \ \ \ \ \ | \cdot (x + 9)\]

\[(5x - 6)(x + 9) \geq 0;\ \ x \neq - 9\]

\[5x - 6 = 0\]

\[x = \frac{6}{5} = 1,2\]

\(\ \)

\[Ответ:x \in ( - \infty;9) \cup \lbrack 1,2;\ + \infty).\]

\[4)\ \frac{4x + 1}{x - 10} \leq 0\ \ \ \ \ \ \ \ \ \ \ | \cdot (x - 10)\]

\[(4x + 1)(x - 10) \leq 0;\ \ \ \ \ x \neq 10\]

\[4x + 1 = 0\]

\[x = - \frac{1}{4} = - 0,25\]

\(\ \)

\[Ответ:x \in \lbrack - 0,25;10)\text{.\ }\]