Решите уравнение: |x+2|-x=6.

\[|x + 2| - x = 6\]

\[\left\{ \begin{matrix} x + 2 - x = 6 \\ x + 2 \geq 0\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 0 \cdot x = 4 \\ x \geq - 2\ \ \ \\ \end{matrix} \right.\ ,\ нет\ корней\]

\[\left\{ \begin{matrix} - x - 2 - x = 6 \\ x + 2 < 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

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

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

\[Ответ:\ - 4.\]