Đáp án:
\(x = \dfrac{2}{3}\) hoặc \(x = 4\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left| {3 - 2x} \right| = x + 1\\
\Leftrightarrow \left\{ \begin{array}{l}
x + 1 \ge 0\\
\left[ \begin{array}{l}
3 - 2x = x + 1\\
3 - 2x = - \left( {x + 1} \right)
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge - 1\\
\left[ \begin{array}{l}
3 - 2x = x + 1\\
3 - 2x = - x - 1
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge - 1\\
\left[ \begin{array}{l}
3 - 1 = x + 2x\\
3 + 1 = - x + 2x
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge - 1\\
\left[ \begin{array}{l}
2 = 3x\\
4 = x
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge - 1\\
\left[ \begin{array}{l}
x = \dfrac{2}{3}\\
x = 4
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{2}{3}\\
x = 4
\end{array} \right.
\end{array}\)
Vậy \(x = \dfrac{2}{3}\) hoặc \(x = 4\)
