Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\left| {2x - 1} \right| < 3\\
\Leftrightarrow - 3 < 2x - 1 < 3\\
\Leftrightarrow - 2 < 2x < 4\\
\Leftrightarrow - 1 < x < 2\\
b,\\
\left| {3x - 2} \right| \le 1\\
\Leftrightarrow - 1 \le 3x - 2 \le 1\\
\Leftrightarrow 1 \le 3x \le 3\\
\Leftrightarrow \frac{1}{3} \le x \le 1\\
c,\\
\left| {3x - 5} \right| > 2\\
\Leftrightarrow \left[ \begin{array}{l}
3x - 5 > 2\\
3x - 5 < - 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x > 7\\
3x < 3
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x > \frac{7}{3}\\
x < 1
\end{array} \right.\\
d,\\
\left| {x - 1} \right| \le \left| {3x + 2} \right|\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left| {x - 1} \right| \le 3x + 2\\
3x + 2 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
\left| {x - 1} \right| \le - 3x - 2\\
3x + 2 < 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- 3x - 2 \le x - 1 \le 3x + 2\\
x \ge - \frac{2}{3}
\end{array} \right.\\
\left\{ \begin{array}{l}
3x + 2 \le x - 1 \le - 3x - 2\\
x < - \frac{2}{3}
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- \frac{1}{4} \le x\\
x \ge - \frac{3}{2}\\
x \ge - \frac{2}{3}
\end{array} \right.\\
\left\{ \begin{array}{l}
x \le - \frac{3}{2}\\
x \le - \frac{1}{4}\\
x < - \frac{2}{3}
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x \ge - \frac{1}{4}\\
x \le - \frac{3}{2}
\end{array} \right.
\end{array}\)
