$\begin{array}{l}
a)\,\,\,\,\left| {2x + 3} \right| = 5\\
\Rightarrow \left[ \begin{array}{l}
2x + 3 = 5\\
2x - 3 = 5
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
2x = 2\\
2x = 8
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 1\\
x = 4
\end{array} \right.\\
b)\,\,\,\left| {2x - 1} \right| = \left| {2x + 3} \right|\\
\Rightarrow \left[ \begin{array}{l}
2x - 1 = 2x + 3\\
2x - 1 = - 2x - 3
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
2x - 2x = 3 + 1\\
2x + 2x = - 3 + 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
0x = 4\,\,(vo\,\,li)\\
4x = - 2\,\,\,
\end{array} \right. \Rightarrow x = \dfrac{{ - 1}}{2}
\end{array}$
