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МатематикаРешебник по алгебре 9 класс Мерзляк Проверь себя №1
Проверь себя №1
\[\boxed{\mathbf{Задание}\mathbf{\ 1.}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[\mathbf{№1.}\]
\[a - b = - 3,6\]
\[a = b - 3,6\]
\[a < b\]
\[\mathbf{Ответ:Б.}\]
\[\mathbf{№2.}\]
\[m > n,\ \ \]
\[- 2m > - 2n \Longrightarrow неверно,\ \ \]
\[- 2m < - 2n\]
\[Ответ:Г.\]
\[\mathbf{№3.}\]
\[0,8 < a < 1,2\]
\[2,4 < 3a < 3,6\]
\[Ответ:Б.\]
\[\mathbf{№4.}\]
\[2 < x < 3\ \ \ \ и\ \ \ \ \ 1 < y < 4\]
\[2 < x < 3 \cdot 1 < y < 4\]
\[2 < xy < 12\]
\[Ответ:В.\]
\[\mathbf{№5.}\]
\[- 18 < y < 12\]
\[- 3 < \frac{1}{6}y < 2\]
\[- 1 < \frac{1}{6}y + 2 < 4\]
\[Ответ:Б.\]
\[\mathbf{№6.}\]
\[a > 0,\ \ b < 0\]
\[a^{2} < b^{2} \Longrightarrow \mathbf{может\ быть\ }\]
\[\mathbf{правильным.}\]
\[\mathbf{Ответ:А.}\]
\[\mathbf{№7.}\]
\[0 \cdot x > - 2 \Longrightarrow x - \mathbf{любое\ число.}\]
\[\mathbf{Ответ:В.}\]
\[\mathbf{№8.}\]
\[(3; + \infty),\ \ x > 3\]
\[\mathbf{Ответ:В.}\]
\[\mathbf{№9.}\]
\[\frac{x}{4} \leq \frac{1}{5}\]
\[\frac{x}{4} - \frac{1}{5} \leq 0\]
\[\frac{5x - 4}{20} \leq 0\ \ \ \ \ | \cdot 20\]
\[5x - 4 \leq 0\]
\[5x \leq 4\]
\[x \leq \frac{4}{5}\]
\[Ответ:В.\]
\[\mathbf{№10.}\]
\[- 3x + 8 \geq 5\]
\[- 3x \geq - 3\]
\[x \leq 1\]
\[\mathbf{Ответ:А.}\]
\[\mathbf{№11.}\]
\[\frac{3x - 5}{2} > \frac{8 - x}{3}\]
\[9x - 15 > 16 - 2x\]
\[11x > 31\]
\[x > \frac{31}{11}\]
\[x > 2\frac{9}{11}\]
\[Ответ:Б.\]
\[\mathbf{№12.}\]
\[\sqrt{14 - 3x}\]
\[14 - 3x \geq 0\]
\[- 3x \geq - 14\]
\[x \leq \frac{14}{3}\]
\[x \leq 4\frac{2}{3}\]
\[2 \cdot 3 \cdot 4 = 24\]
\[Ответ:Г.\]
\[\mathbf{№13.}\]
\[\left\{ \begin{matrix} x \geq - 3 \\ x \leq - 2 \\ \end{matrix} \right.\ ,\ \ x \in \lbrack - 3;\ - 2\rbrack\]
\[\left\{ \begin{matrix} x > - 3 \\ x > - 2 \\ \end{matrix} \right.\ ,\ \ x \in ( - 2; + \infty)\]
\[\left\{ \begin{matrix} x \geq - 3 \\ x \leq - 3 \\ \end{matrix} \right.\ ,\ \ x = - 3\]
\[\left\{ \begin{matrix} x \geq - 2 \\ x \leq - 3 \\ \end{matrix} \right.\ \]
\[Ответ:Г.\]
\[\mathbf{№14.}\]
\[\left\{ \begin{matrix} x - 1 > 2x - 3 \\ 4x + 5 > x + 17 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} - x > - 2 \\ 3x > 12 \\ \end{matrix} \right.\ \text{\ \ }\]
\[\text{\ \ \ \ }\left\{ \begin{matrix} x < 2 \\ x > 4 \\ \end{matrix} \right.\ ,\ \ \varnothing\]
\[Ответ:А.\]
\[\mathbf{№15.}\]
\[\left\{ \begin{matrix} 8 - 7x > 3x - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 2 \cdot (3x - 2,6) \leq - 2 \cdot ( - 2,6) \\ \end{matrix} \right.\ \text{\ \ \ }\]
\[\text{\ \ \ \ \ }\left\{ \begin{matrix} - 10x > - 10\ \ \ \ \ \ \\ - 6x + 5,2 \leq 5,2 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x < 1\ \ \ \ \ \\ - 6x \leq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x < 1 \\ x \geq 0 \\ \end{matrix} \right.\ \]
\[\mathbf{Ответ:Г.}\]
\[\mathbf{№16.}\]
\[\left\{ \begin{matrix} x - \frac{x - 2}{3} \geq \frac{x - 3}{4} - \frac{x - 1}{2} \\ 1 - 0,5x > x - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} \frac{3x - x + 2}{3} \geq \frac{2x - 6 - 4x + 4}{8} \\ - 1,5x > - 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} \frac{2x + 2}{3} \geq \frac{- 2x - 2}{8} \\ x < \frac{10}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ }\]
\[\text{\ \ \ }\left\{ \begin{matrix} 16x + 16 \geq - 6x - 6 \\ x < \frac{10}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} 22x \geq - 22 \\ x < 3\frac{1}{3}\text{\ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ }\left\{ \begin{matrix} x \geq - 1 \\ x < 3\frac{1}{3} \\ \end{matrix} \right.\ \]
\[\mathbf{Ответ:В.}\]
\[\mathbf{№17.}\]
\[- 3 < \frac{1 - 2x}{5} - 2 < 1\]
\[- 1 < \frac{1 - 2x}{5} < 3\]
\[- 5 < 1 - 2x < 15\]
\[- 6 < - 2x < 14\]
\[- 7 < x < 3\]
\[x \in ( - 7;3).\]
\[Ответ:Б.\]
\[\mathbf{№18.}\]
\[2x² + 6x + a = 0\]
\[D = 36 - 8a\]
\[36 - 8a < 0\]
\[- 8a < - 36\]
\[a > 4,5\]
\[Ответ:Б.\]
