Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 20

$x=-6$

Using the properties of equality, the solution to the given equation, $ 4x+3=-21 $, is \begin{array}{l} 4x+3-3=-21-3 \\\\ 4x=-24 \\\\ \dfrac{4x}{4}=\dfrac{-24}{4} \\\\ x=-6 .\end{array} Checking: \begin{array}{l} 4(-6)+3=-21 \\\\ -24+3=-21 \\\\ -21=-21 \text{ (TRUE)} .\end{array} Hence, the solution is $ x=-6 .$