Решите уравнение: |x|-|x-3|=4.

\[|x| - |x - 3| = 4\]

\[1)\ \left\{ \begin{matrix} x < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - x + x - 3 = 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < 0\ \ \ \ \ \\ 0 \cdot x = 7 \\ \end{matrix} \right.\ ,\ нет\ корней\]

\[2)\ \left\{ \begin{matrix} x + x - 3 = 4 \\ 0 \leq x \leq 3\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x = 7\ \ \ \ \ \\ 0 \leq x \leq 3 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x = 3,5\ \ \ \ \ \\ 0 \leq x \leq 3 \\ \end{matrix} \right.\ ,\ нет\ корней\]

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

\[\left\{ \begin{matrix} x > 3\ \ \ \ \ \ \\ 0 \cdot x = 1 \\ \end{matrix} \right.\ ,\ \ \ нет\ корней\]

\[Ответ:нет\ корней.\]