ГДЗ по алгебре 9 класс Мерзляк Задание 203

\[\boxed{\text{203\ (203).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (x - 3) \cdot (x + 4) \leq 0\]

\[x - 3 = 0\ \ \ или\ \ \ x + 4 = 0\]

\[x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 4\]

\(\ \)

\[при\ x \leq - 4\ функция\ \]

\[принимает\ неотрицательные\ \]

\[значения,\ \ \]

\[при\ x \in \lbrack - 4;3\rbrack -\]

\[неположительные\ значения,\ \]

\[при\ x \geq 3 - неотрицательные.\]

\[Ответ:x \in \lbrack - 4;3\rbrack.\]

\[2)\ (x + 1) \cdot (2x - 7) > 0\]

\[x + 1 = 0\ \ \ или\ \ \ 2x - 7 = 0\]

\[x = - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 3,5\]

\[Ответ:x \in ( - \infty;\ - 1) \cup (3,5;\ + \infty).\]

\[3)\ \frac{x - 8}{x - 1} > 0\ \ \ \ \ \ \ \ \ \ \ | \cdot (x - 1)\]

\[(x - 8) \cdot (x - 1) > 0;\ \ \ \ \ x \neq 1\]

\[x - 8 = 0\ \ \ или\ \ \ x - 1 = 0\]

\[x = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 1\]

\[Ответ:x \in ( - \infty;1) \cup (8;\ + \infty).\]

\[4)\ \frac{3x + 6}{x - 9} < 0\ \ \ \ \ \ \ | \cdot (x - 9)\]

\[(3x + 6) \cdot (x - 9) < 0;\ \ x \neq 9\]

\[3x + 6 = 0\ \ \ или\ \ \ x - 9 = 0\]

\[x = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 9\]

\(\ \)

\[Ответ:x \in ( - 2;9).\]

\[5)\ \frac{2x - 1}{x + 2} \leq 0\ \ \ \ \ \ \ \ | \cdot (x + 2)\]

\[(2x - 1) \cdot (x + 2) \leq 0;\ x \neq - 2\]

\[2x - 1 = 0\ \ \ или\ \ \ x + 2 = 0\]

\[x = 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 2\]

\(\ \)

\[Ответ:x \in ( - 2;0,5\rbrack.\]

\[6)\ \frac{5x + 4}{x - 6} \geq 0\ \ \ \ \ \ \ \ \ \ \ \ | \cdot (x - 6)\]

\[(5x + 4) \cdot (x - 6) \geq 0;\ \ \ \ \ \ x \neq 6\]

\[5x + 4 = 0\ \ \ или\ \ \ x - 6 = 0\]

\[x = - 0,8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 6\]

\(\ \)

\[Ответ:x \in ( - \infty;\ - 0,8\rbrack \cup ( - 6;\ + \infty)\text{.\ }\]