Answer
$$\left( { - 2, - 1} \right) \cup \left( {2,3} \right)$$
Work Step by Step
$$\eqalign{
& 3 < \left| {2x - 1} \right| < 5 \cr
& {\text{The solution of the inequality is any number that is a solution }} \cr
& {\text{of both of these inequalities}}: \cr
& 3 < \left| {2x - 1} \right|{\text{ and }}\left| {2x - 1} \right| < 5 \cr
& \cr
& {\text{Solving }}3 < \left| {2x - 1} \right|,{\text{use the property }}\left| x \right| \geqslant a \Leftrightarrow x \leqslant - a{\text{ or }}x \geqslant a \cr
& 2x - 1 < - 3{\text{ or }}2x - 1 > 3 \cr
& 2x < - 2{\text{ or }}2x > 4 \cr
& x < - 1{\text{ or }}x > 2 \cr
& {\text{Express in form of intervals}} \cr
& \left( { - \infty , - 1} \right) \cup \left( {2,\infty } \right) \cr
& \cr
& {\text{Solving }}\left| {2x - 1} \right| < 5,{\text{use the property }}\left| x \right| \leqslant a \Leftrightarrow - a \leqslant x \leqslant a \cr
& - 5 < 2x - 1 < 5 \cr
& - 4 < 2x < 6 \cr
& - 2 < x < 3 \cr
& {\text{Express in form of intervals}} \cr
& \left( { - 2,3} \right) \cr
& \cr
& {\text{Intersecting both solutions}} \cr
& \left[ {\left( { - \infty , - 1} \right) \cup \left( {2,\infty } \right)} \right] \cap \left( { - 2,3} \right) \cr
& {\text{We obtain}} \cr
& \left( { - 2, - 1} \right) \cup \left( {2,3} \right) \cr
& {\text{The solution set is }} \cr
& - 2 < x < - 1{\text{ or }}2 < x < 3 \cr} $$