Решите неравенство: |x+4|+|x-2|>6.

\[|x + 4| + |x - 2| > 6\]

\[1)\ \left\{ \begin{matrix} x < - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - x - 4 + 2 - x > 6 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x < - 4\ \ \\ - 2x > 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < - 4 \\ x < - 4 \\ \end{matrix} \right.\ \text{\ \ \ \ }( - \infty; - 4)\]

\[2)\ \left\{ \begin{matrix} - 4 \leq x \leq 2\ \ \ \ \ \ \ \ \ \ \ \ \\ x + 4 + 2 - x > 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 4 \leq x \leq 2 \\ 0 \cdot x > 0\ \ \ \ \ \\ \end{matrix} \right.\ \ \ \ \ \ нет\ решений\]

\[3)\ \left\{ \begin{matrix} x > 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x + 4 + x - 2 > 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x > 2\ \ \\ 2x > 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x > 2 \\ x > 2 \\ \end{matrix} \right.\ \text{\ \ \ \ }(2; + \infty)\]

\[Ответ:( - \infty; - 4) \cup (2; + \infty).\]