Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 183: 10

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

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