Решите неравенство: |3x+16|-|2x-14|>8.

\[|3x + 16| - |2x - 14| > 8\]

\[1)\ \left\{ \begin{matrix} x < - 5\frac{1}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ - 3x - 16 + 2x - 14 > 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < - 5\frac{1}{3} \\ - x > 38\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < - 5\frac{1}{3} \\ x < - 38\ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[( - \infty; - 38)\]

\[2)\ \left\{ \begin{matrix} - 5\frac{1}{3} \leq x \leq 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + 16 + 2x - 14 > 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 5\frac{1}{3} \leq x \leq 7\ \ \ \ \ \ \ \ \ \ \\ 5x > 6;\ \ \ \ \ \ \ \ \ \ x > \frac{6}{5} \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left( \frac{6}{5};7 \right\rbrack\]

\[3)\ \left\{ \begin{matrix} x > 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + 16 - 2x + 14 > 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x > 7\ \ \ \ \ \ \\ x > - 22 \\ \end{matrix} \right.\ \ \ \ \ \ \ \ (7; + \infty)\]

\[Ответ:( - \infty;\ - 38) \cup \left( \frac{6}{5};\ + \infty \right).\]