Решите уравнение: |x|+|x-3|=4.

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

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

\[\left\{ \begin{matrix} x < 0\ \ \ \ \ \\ - 2x = 1 \\ \end{matrix} \right.\ ,\ \ x = - \frac{1}{2}\]

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

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

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

\[\left\{ \begin{matrix} x > 3\ \ \\ 2x = 7 \\ \end{matrix} \right.\ ,\ \ x = 3,5\]

\[Ответ:\ - \frac{1}{2};\ \ 3,5.\]