Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 44

$x=\dfrac{25}{3}$

Multiplying both sides by the $LCD= 12 ,$ the value of the variable that satisfies the given equation, $ -2+\dfrac{x+3}{4}=\dfrac{5}{6} ,$ is \begin{array}{l}\require{cancel} 12(-2)+3(x+3)=2(5) \\\\ -24+3x+9=10 \\\\ 3x=10+24-9 \\\\ 3x=25 \\\\ x=\dfrac{25}{3} .\end{array}