Решите уравнение: |x|-|x-5|=6.

\[|x| - |x - 5| = 6\]

\[1)\ \left\{ \begin{matrix} x < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - x - 5 + x = 6 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x < 0\ \ \ \ \ \ \ \ \\ 0 \cdot x = 11 \\ \end{matrix}\ \ \ \ \ \ \ \ \ \ нет\ корней. \right.\ \]

\[2)\ \left\{ \begin{matrix} 0 \leq x \leq 5\ \ \ \ \ \ \ \\ x - 5 + x = 6 \\ \end{matrix}\text{\ \ \ \ } \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 0 \leq x \leq 5 \\ 2x = 11\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} 0 \leq x \leq 5 \\ x = 5,5\ \ \ \ \\ \end{matrix}\ \ \ \ \ нет\ корней. \right.\ \]

\[3)\left\{ \begin{matrix} x > 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - x + 5 = 6\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x > 5\ \ \ \ \ \ \\ 0 \cdot x = 1 \\ \end{matrix}\ \ \ \ \ \ \ \ \ \ \ нет\ корней. \right.\ \]

\[Ответ:нет\ корней.\]