Đáp án:
$\begin{array}{l}
\frac{{x - 1}}{{2x + 1}} < \frac{1}{3}\\
\Leftrightarrow \frac{{x - 1}}{{2x + 1}} - \frac{1}{3} < 0\\
\Leftrightarrow \frac{{3\left( {x - 1} \right) - \left( {2x + 1} \right)}}{{3\left( {2x + 1} \right)}} < 0\\
\Leftrightarrow \frac{{3x - 3 - 2x - 1}}{{3\left( {2x + 1} \right)}} < 0\\
\Leftrightarrow \frac{{x - 4}}{{3\left( {2x + 1} \right)}} < 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 4 < 0\\
2x + 1 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 4 > 0\\
2x + 1 < 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < 4\\
x > - \frac{1}{2}
\end{array} \right.\\
\left\{ \begin{array}{l}
x > 4\\
x < - \frac{1}{2}
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow - \frac{1}{2} < x < 4
\end{array}$
