Chapter 1 - Expressions, Equations, and Inequalities - 1-6 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 46: 48

$h=$ $\dfrac{5}{2}$

You are given the equation $7|8-3h|=21h-49$. Divide both sides by $7$: $7|8-3h|=21h-49$ $|8-3h|=$ $\dfrac{21h-49}{7}$ $8-3h=3h-7$ Separate into two equations: $8-3h=3h-7$ $or$ $8-3h=-(3h-7)$ Solve: $8-3h=3h-7$ $8=6h-7$ $15=6h$ $h=$ $\dfrac{5}{2}$ Second equation: $8-3h=-(3h-7)$ $8-3h=-3h+7$ $8=7$ $No$ $solution$ The solution is $h=$ $\dfrac{5}{2}$