Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 34

$x=-93$

Multiplying both sides by the $LCD= 30 ,$ the value of the variable that satisfies the given equation, $ \dfrac{x-2}{5}-\dfrac{x+3}{6}=-4 ,$ is \begin{array}{l}\require{cancel} 6(x-2)-5(x+3)=30(-4) \\\\ 6x-12-5x-15=-120 \\\\ 6x-5x=-120+12+15 \\\\ x=-93 .\end{array}