Решите систему неравенств: 26-x<25; 2x+7<13

Ответ:

\[\ \left\{ \begin{matrix} 26 - x < 25 \\ 2x + 7 < 13 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} - x < - 1 \\ 2x < 6\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x > 1 \\ x < 3 \\ \end{matrix} \right.\ \]

\[\]

\[Ответ:x \in (1;3).\]

\[\left\{ \begin{matrix} 1 - 5x < 4 \cdot (1 - x) \\ 3,5 + \frac{x}{4} \geq 2x\text{\ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 1 - 5x < 4 - 4x \\ 3,5 \geq 2x - \frac{x}{4}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - x < 3\ \ \ \ \ \ \ \ \ \ \ \\ 3,5 \geq 1,75x\ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x > - 3 \\ x \leq 2\ \ \ \\ \end{matrix} \right.\ \]

\[\mathbf{Ответ}:x = - 2;\ - 1;0;1;2.\]

\[\sqrt{15 - 5m} + \sqrt{4 + m}\]

\[\left\{ \begin{matrix} 15 - 5m \geq 0 \\ 4 + m \geq 0\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} - 5m \geq - 15 \\ m \geq - 4\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} m \leq 3\ \ \ \ \\ m \geq - 4 \\ \end{matrix} \right.\ \]

\[Ответ:\ выражение\ имеет\ смысл\ при\ m \in \lbrack - 4;3\rbrack\text{.\ }\]

\[6x + 11 > \frac{b}{4}\text{\ \ \ \ \ \ }x \in (1; + \infty)\]

\[6x > \frac{b}{4} - 11\ \]

\[6x > \frac{b - 44}{4}\]

\[x > \frac{b - 44}{24}\]

\[1 < \frac{b - 44}{24} < + \infty\]

\[24 < b - 44 < + \infty\]

\[68 < b < + \infty\]

\[Ответ:b \in (68; + \infty).\]

\[\ 4^{11} \cdot 4^{- 9} = 4^{11 + ( - 9)} = 4^{2} = 16\]