Đáp án:
$\begin{array}{l}
\frac{2}{{x - 1}} \le \frac{3}{{1 - 2x}}\left( {dkxd:x \ne 1;x \ne \frac{1}{2}} \right)\\
\Rightarrow \frac{2}{{x - 1}} - \frac{3}{{1 - 2x}} \le 0\\
\Rightarrow \frac{{2\left( {2x - 1} \right) + 3\left( {x - 1} \right)}}{{\left( {x - 1} \right)\left( {2x - 1} \right)}} \le 0\\
\Rightarrow \frac{{4x - 2 + 3x - 3}}{{\left( {x - 1} \right)\left( {2x - 1} \right)}} \le 0\\
\Rightarrow \frac{{7x - 5}}{{\left( {x - 1} \right)\left( {2x - 1} \right)}} \le 0\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
7x - 5 \le 0\\
\left( {x - 1} \right)\left( {2x - 1} \right) > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
7x - 5 \ge 0\\
\left( {x - 1} \right)\left( {2x - 1} \right) < 0
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \le \frac{5}{7}\\
x > 1/x < \frac{1}{2}
\end{array} \right.\\
\left\{ \begin{array}{l}
x \ge \frac{5}{7}\\
\frac{1}{2} < x < 1
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x < \frac{1}{2}\\
\frac{5}{7} \le x < 1
\end{array} \right.
\end{array}$
