Решите уравнение: |2x+4|-x=3.

Ответ:

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

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

\[\left\{ \begin{matrix} x = - 1\ \ \\ 2x > - 4 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x = - 1 \\ x > - 2 \\ \end{matrix}\ \ \Longrightarrow \ x = - 1 \right.\ \]

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

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

\[\left\{ \begin{matrix} x = - 2\frac{1}{3} \\ x < - 2\ \ \\ \end{matrix}\ \Longrightarrow x = - 2\frac{1}{3} \right.\ \]

\[Ответ:\ - 1;\ - 2\ \frac{1}{3}.\]