Giải thích các bước giải:
\(\begin{array}{l}
a,\\
\left| {2x - 1} \right| < 3x + 5\\
\Leftrightarrow \left\{ \begin{array}{l}
3x + 5 > 0\\
- \left( {3x + 5} \right) < 2x - 1 < 3x + 5
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x > - \frac{5}{3}\\
2x - 1 > - 3x - 5\\
3x + 5 > 2x - 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x > - \frac{5}{3}\\
x > - \frac{4}{5}\\
x > - 6
\end{array} \right.\\
\Leftrightarrow x > - \frac{4}{5}\\
b,\\
\frac{{x + 1}}{{2x + 1}} < \frac{{x - 3}}{{2x - 3}}\,\,\,\,\,\,\,\,\,\,\left( {x \ne - \frac{1}{2};\,\,\,\,x \ne \frac{3}{2}} \right)\\
\Leftrightarrow \frac{{x + 1}}{{2x + 1}} - \frac{{x - 3}}{{2x - 3}} < 0\\
\Leftrightarrow \frac{{\left( {x + 1} \right)\left( {2x - 3} \right) - \left( {x - 3} \right)\left( {2x + 1} \right)}}{{\left( {2x + 1} \right)\left( {2x - 3} \right)}} < 0\\
\Leftrightarrow \frac{{\left( {2{x^2} - x - 3} \right) - \left( {2{x^2} - 5x - 3} \right)}}{{\left( {2x + 1} \right)\left( {2x - 3} \right)}} < 0\\
\Leftrightarrow \frac{{4x}}{{\left( {2x + 1} \right)\left( {2x - 3} \right)}} < 0\\
\Leftrightarrow \left[ \begin{array}{l}
x < - \frac{1}{2}\\
0 < x < \frac{3}{2}
\end{array} \right.\\
c,\\
\frac{2}{x} + \frac{1}{{x - 2}} > 0\,\,\,\,\,\,\,\,\left( \begin{array}{l}
x \ne 0\\
x \ne 2
\end{array} \right)\\
\Leftrightarrow \frac{{2\left( {x - 2} \right) + x}}{{x\left( {x - 2} \right)}} > 0\\
\Leftrightarrow \frac{{3x - 4}}{{x\left( {x - 2} \right)}} > 0\\
\Leftrightarrow \left[ \begin{array}{l}
x > 2\\
0 < x < \frac{4}{3}
\end{array} \right.
\end{array}\)
