ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 892

\[1)\ |2x - 5| \leq 3\]

\[- 3 \leq 2x - 5 \leq 3\]

\[2 \leq 2x \leq 8\]

\[1 \leq x \leq 4.\]

\[Ответ:\ \ x \in \lbrack 1;\ 4\rbrack.\]

\[2)\ |5x - 9| > 4\]

\[5x - 9 < - 4\]

\[5x < 5\]

\[x < 1.\ \]

\[5x - 9 > 4\]

\[5x > 13\]

\[x > 2,6.\]

\[Ответ:\ \ \]

\[x \in ( - \infty;\ 1) \cup (2,6;\ + \infty).\]

\[3)\ |2 - 3x| < x + 1\]

\[2 - 3x > - x - 1\]

\[2x < 3\]

\[x < 1,5.\]

\[2 - 3x < x + 1\]

\[4x > 1\]

\[x > 0,25.\]

\[Ответ:\ \ x \in (0,25;\ 1,5).\]

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

\[1 + 2x \leq - 3 + x\]

\[2x - x \leq - 4\ \ \ \]

\[x \leq - 4.\]

\[1 + 2x \geq 3 - x\]

\[3x \geq 2\]

\[x \geq \frac{2}{3}.\]

\[Ответ:\ \ \]

\[x \in ( - \infty;\ - 4\rbrack \cup \left\lbrack \frac{2}{3};\ + \infty \right).\]