Решите систему неравенств: 15-x<14; 4-2x<5

Ответ:

\[\ \left\{ \begin{matrix} 15 - x < 14 \\ 4 - 2x < 5\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} - x < - 1 \\ - 2x < 1\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x > 1\ \ \ \ \ \ \ \\ x > - 0,5 \\ \end{matrix} \right.\ \]

\[Ответ:\ x \in (1;\ + \infty).\]

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

\[\left\{ \begin{matrix} 5 - 10x < 2x - 4 \\ 2,5 \geq x - \frac{x}{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 12x < - 9 \\ 0,5x \leq 2,5\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x > \frac{9}{12} \\ x \leq 5\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x > 0,75 \\ x \leq 5\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\]

\[Ответ:\ \ x = 1;2;3;4;5.\]

\[\sqrt{12 - 3a} + \sqrt{a + 2}\]

\[\left\{ \begin{matrix} 12 - 3a \geq 0 \\ a + 2 \geq 0\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} - 3a \geq - 12 \\ a \geq - 2\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} a \leq 4\ \ \ \ \\ a \geq - 2 \\ \end{matrix} \right.\ \]

\[Ответ:выражение\ имеет\ смысл\ при\ \]

\[a \in \lbrack - 2;4\rbrack\text{.\ }\]

\[5x - 1 < \frac{a}{4}\text{\ \ \ \ \ \ }x \in ( - \infty;2)\]

\[5x < \frac{a}{4} + 1\]

\[5x < \frac{a + 4}{4}\]

\[x < \frac{a + 4}{20}\]

\[- \infty < \frac{a + 4}{20} < 2\]

\[- \infty < a + 4 < 40\]

\[- \infty < a < 36\]

\[Ответ:\ \ a \in ( - \infty;36).\]

\[\frac{1}{8}x \leq 2\]

\[x \leq 16.\]