Answer
$[\frac{3}{4},\frac{15}{8}]$
Work Step by Step
We are given the inequality $\frac{1}{2}\leq\frac{2}{3}x\leq\frac{5}{4}$. In order to solve, multiply all terms by 12 (the greatest common denominator of all terms).
$6\leq8x\leq15$
Divide all terms by 8.
$\frac{6}{8}\leq x\leq\frac{15}{8}$
$\frac{3}{4}\leq x\leq\frac{15}{8}$