Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 53

$x=28$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{2(x-1)}{3}=\dfrac{3(x+2)}{5} ,$ is \begin{array}{l}\require{cancel} 2(5)(x-1)=3(3)(x+2) \\\\ 10x-10=9x+18 \\\\ 10x-9x=18+10 \\\\ x=28 .\end{array}