Answer
$(6,12)$
Work Step by Step
$-2 \lt \frac{1}{2}x-5 \lt 1$
Using inequality properties, multiply all parts by 2.
$2(-2) \lt 2(\frac{1}{2}x-5) \lt (1) 2$
$-4 \lt 2(\frac{1}{2}x-5) \lt 2$
Using distributive property,
$-4 \lt 2(\frac{1}{2}x)-2(5) \lt 2$
$-4 \lt x-10 \lt 2$
Add 10 to all parts,
$-4+10 \lt x-10+10 \lt 2+10$
$6 \lt x\lt 12$
Interval Notation: $(6,12)$