Intermediate Algebra (12th Edition)

$[\frac{3}{4},\frac{15}{8}]$
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. $\frac{6}{8}\leq x\leq\frac{15}{8}$ $\frac{3}{4}\leq x\leq\frac{15}{8}$