Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 45

$x=-\dfrac{53}{2}$

Multiplying both sides by the $LCD= 10 ,$ the value of the variable that satisfies the given equation, $ -3-\dfrac{x+4}{5}=\dfrac{3}{2} ,$ is \begin{array}{l}\require{cancel} 10(-3)-2(x+4)=5(3) \\\\ -30-2x-8=15 \\\\ -2x=15+30+8 \\\\ -2x=53 \\\\ x=\dfrac{53}{-2} \\\\ x=-\dfrac{53}{2} .\end{array}