Answer
The solution set is $~~(\frac{9}{2}, 5)\cup (5,\frac{11}{2})$
Work Step by Step
$0 \lt \vert x-5 \vert \lt \frac{1}{2}$
Case 1:
$-\frac{1}{2} \lt x-5 \lt 0$
$\frac{9}{2} \lt x \lt 5$
Case 2:
$0 \lt x-5 \lt \frac{1}{2}$
$5 \lt x \lt \frac{11}{2}$
The solution set is $~~(\frac{9}{2}, 5)\cup (5,\frac{11}{2})$
