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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 183
Задание 183
\[\boxed{\text{183\ (183).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[1)\left\{ \begin{matrix} x - 4 < 0 \\ 2x \geq - 6\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x < 4\ \ \ \\ x \geq - 3 \\ \end{matrix} \right.\ \]
\[Ответ:\lbrack - 3;4).\]
\[2)\ \left\{ \begin{matrix} x - 2 > 3\ \ \ \ \\ - 3x < - 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x > 5 \\ x > 4 \\ \end{matrix} \right.\ \]
\[Ответ:(5;\ + \infty).\]
\[3)\ \left\{ \begin{matrix} x + 6 > 2 \\ \frac{x}{4} < 2\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x > - 4 \\ x < 8\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:( - 4;8)\text{.\ }\]
\[4)\ \left\{ \begin{matrix} 6x + 3 \geq 0 \\ 7 - 4x < 7 \\ \end{matrix}\text{\ \ } \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} 6x \geq - 3 \\ - 4x < 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x \geq - \frac{1}{2} \\ x > 0\ \ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:(0;\ + \infty).\]
\[5)\ \left\{ \begin{matrix} 10x - 1 \geq 3\ \ \ \ \ \ \ \ \\ 7 - 3x \geq 2x - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} 10x \geq 4\ \ \ \ \ \ \ \\ - 5x \geq - 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \geq \frac{2}{5} \\ x \leq 2 \\ \end{matrix} \right.\ \]
\[Ответ:\ \lbrack 0,4;2\rbrack.\]
\[6)\ \left\{ \begin{matrix} x - 2 < 1 + 3x \\ 5x - 7 \leq x + 9 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} - 2x < 3 \\ 4x \leq 16 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x > - 1,5 \\ x \leq 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:( - 1,5;4\rbrack.\]
\[7)\ \left\{ \begin{matrix} 3x - 6 \leq x - 1\ \ \ \ \ \\ 11x + 13 < x + 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} 2x \leq 5\ \ \ \ \ \ \ \ \ \\ 10x < - 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \leq 2,5 \\ x < - 1 \\ \end{matrix} \right.\ \]
\[Ответ:( - \infty;\ - 1).\]
\[8)\ \left\{ \begin{matrix} 5x + 14 \geq 18 - x \\ 1,5x + 1 < 3x - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 6x \geq 4\ \ \ \ \ \ \ \ \ \ \\ - 1,5x < - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \geq \frac{2}{3} \\ x > 2 \\ \end{matrix} \right.\ \]
\[Ответ:(2;\ + \infty).\]
\[9)\ \left\{ \begin{matrix} 4x + 19 \leq 5x - 1 \\ 10x < 3x + 21\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[\ \left\{ \begin{matrix} - x \leq - 20 \\ 7x < 21\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 20 \\ x < 3\ \ \\ \end{matrix} \right.\ \]
\[Ответ:\ \varnothing.\]
\[\boxed{\text{183.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \left\{ \begin{matrix} x + y - xy = 1 \\ x + y + xy = 9 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x + y - xy + x + y + xy = 10 \\ x + y - xy - x - y - xy = - 8 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 2x + 2y = 10\ \ \ \ \ |\ :2 \\ - 2xy = - 8\ \ \ \ \ \ \ \ \ \ \ |\ :2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x + y = 5 \\ xy = 4\ \ \ \ \ \\ \end{matrix} \right.\ \]
\[x = 5 - y\]
\[5y - y^{2} - 4 = 0\]
\[y_{1} + y_{2} = 5,\ \ y_{1} = 4\]
\[y_{1}y_{2} = 4,\ \ y_{2} = 1\]
\[\left\{ \begin{matrix} y = 4 \\ x = 1 \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} y = 1 \\ x = 4 \\ \end{matrix} \right.\ \]
\[Ответ:(1;4),\ (4;1).\]
\[2)\ \left\{ \begin{matrix} 3xy + 2x = - 4 \\ 3xy + y = - 8\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} 3xy + 2x - 3xy - y = 4 \\ 3xy + 2x = - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 2x - y = 4\ \ \ \ \ \ \ \ \\ 3\text{xy} + 2x = - 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} y = 2x - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x \cdot (2x - 4) + 2x + 4 = 0 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 2x - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 6x^{2} - 12x + 2x + 4 = 0\ \ \ \ |\ :2 \\ \end{matrix} \right.\ \]
\[3x^{2} - 5x + 2 = 0\]
\[D = 25 - 24 = 1\]
\[x_{1,2} = \frac{5 \pm 1}{6}\]
\[\left\{ \begin{matrix} x = 1\ \ \ \\ y = - 2 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \ \left\{ \begin{matrix} x = \frac{2}{3}\text{\ \ \ \ \ } \\ y = - \frac{8}{3} \\ \end{matrix} \right.\ \]
\[Ответ:(1;\ - 2);\ \left( \frac{2}{3};\ - \frac{8}{3} \right).\]
