Answer
$(\frac{5}{4},\frac{11}{4})$
Work Step by Step
$\frac{1}{2} \lt x - \frac{3}{4} \lt 2$
Using properties of inequalities,
$\frac{1}{2} +\frac{3}{4} \lt x - \frac{3}{4} +\frac{3}{4} \lt 2 +\frac{3}{4}$
$\frac{2+3}{4} \lt x \lt \frac{8+3}{4}$
$\frac{5}{4} \lt x \lt \frac{11}{4}$
Interval Notation : $(\frac{5}{4},\frac{11}{4})$