$\left\{ {\left| {\frac{x}{2}} \right| + \frac{1}{2}} \right\} = \left\{ 3 \right\} \Rightarrow \left| {\frac{x}{2}} \right| + \frac{1}{2} = 3 \Rightarrow \left| {\frac{x}{2}} \right| = 3 - \frac{1}{2} = \frac{5}{2}$
$\left| {\frac{x}{2}} \right| = \frac{5}{2} \Rightarrow \left\{ {\begin{array}{*{20}{c}}
{\frac{x}{2} = \frac{5}{2} \Rightarrow x = 5} \\
{\frac{x}{2} = - \frac{5}{2} \Rightarrow x = - 5}
\end{array}} \right.$