Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 95: 112

$x=-2$

Multiplying both sides by the $LCD= 12 $, then the solution to the given equation, $ \dfrac{5x+3}{4}+\dfrac{25}{12}=\dfrac{5+2x}{3} $, is \begin{array}{l} 3(5x+3)+1(25)=4(5+2x) \\\\ 15x+9+25=20+8x \\\\ 15x-8x=20-9-25 \\\\ 7x=-14 \\\\ x=-\dfrac{14}{7} \\\\ x=-2 .\end{array}