Answer
The solution set is {$-4,4$}
Work Step by Step
$5-|\frac{1}{2}x|=3$ Isolate the absolute value
$-|\frac{1}{2}x|=3-5$
$-|\frac{1}{2}x|=-2$
$|\frac{1}{2}x|=2$
$\frac{1}{2}x=2$ or $\frac{1}{2}x=-2$
$x=2\cdot2$ or $x=-2\cdot2$
$x=4$ or $x=-4$
The solution set is {$-4,4$}.