Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 39

$x=-\dfrac{8}{5}$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{3}{2x-1}=\dfrac{2}{3x+2} ,$ is \begin{array}{l}\require{cancel} 3(3x+2)=2(2x-1) \\\\ 9x+6=4x-2 \\\\ 9x-4x=-2-6 \\\\ 5x=-8 \\\\ x=-\dfrac{8}{5} .\end{array}