Решите уравнение: |2x-3|-|x+2|=4x+5.

\[|2x - 3| - |x + 2| = 4x + 5\]

\[1)\ \left\{ \begin{matrix} x < - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3 - 2x + x + 2 = 4x + 5 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[2)\ \left\{ \begin{matrix} - 2 \leq x \leq 1,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3 - 2x - x - 2 = 4x + 5 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} - 2 \leq x \leq 1,5 \\ - 7x = 4\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 2 \leq x \leq 1,5 \\ x = - \frac{4}{7}\text{\ \ \ \ \ \ \ \ \ \ } \\ \end{matrix}\ \ \ \ \ \ x = - \frac{4}{7} \right.\ \]

\[3)\ \left\{ \begin{matrix} x > 1,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - 3 - x - 2 = 4x + 5 \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[Ответ:\ - \frac{4}{7}.\]