Chapter 1 - Solving Linear Equations - 1.4 - Solving Absolute Value Equations - Exercises - Page 34: 59

$x=1~~~~\text{or}~~~~x=-5$

$$8|x+2|-6=5|x+2|+3$$ $$8|x+2|-5|x+2|=6+3$$ $$(8-5)|x+2|=9$$ $$3|x+2|=9$$ $$|x+2|=3$$ $$x+2=3~~~~\text{or}~~~~x+2=-3$$ $$x=3-2=1~~~~\text{or}~~~~x=-3-2=-5$$ Answer is found first by solving equation for $|x+2|$ and then solving for $x$.