Решите уравнение: |x+2|+|x-5|=7.

\[|x + 2| + |x - 5| = 7\]

\[1)\ \left\{ \begin{matrix}
x < - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
- x - 2 - x + 5 = 7 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

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

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

\[2)\ \left\{ \begin{matrix}
- 2 \leq x \leq 5\ \ \ \ \ \ \ \ \ \ \ \\
x + 5 - x + 5 = 7 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
- 2 \leq x \leq 5 \\
0 \cdot x = 0\ \ \ \ \ \\
\end{matrix} \right.\ \ \ \ x \in \lbrack - 2;5\rbrack\]

\[3)\ \left\{ \begin{matrix}
x > 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
x + 2 + x - 5 = 7 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x > 5\ \ \ \ \\
2x = 10 \\
\end{matrix} \right.\ \text{\ \ \ \ \ }\]

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

\[Ответ:\ x \in \lbrack - 2;5\rbrack.\]