Chapter 1 - Expressions, Equations, and Inequalities - 1-6 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 46: 50

$x=-1$ or $x=-3$

You are given the equation $6|2x+5|=6x+24$. Divide both sides by $6$: $6|2x+5|=6x+24$ $|2x+5|=$ $\dfrac{6x+24}{6}$ $|2x+5|=x+4$ Separate into two equations: $2x+5=x+4$ $or$ $2x+5=-(x+4)$ Solve: $2x+5=x+4$ $x+5=4$ $x=-1$ Second equation: $2x+5=-(x+4)$ $2x+5=-x-4$ $3x+5=-4$ $3x=-9$ $x=-3$ The solutions are $x=-1$ or $x=-3$