# Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 211: 17

$r=3$ or $r=13$

#### Work Step by Step

We know that when we evaluate an absolute value, the result will be positive, regardless of the sign of what is inside of the absolute value bars. Thus, we consider that the variable could be either a positive or a negative number. $|r-8|=5\longrightarrow$ definition of absolute value $r-8=-5\ or\ r-8=5\longrightarrow$ solve each equation $r-8=-5\longrightarrow$ add 8 to each side $r-8+8=-5+8\longrightarrow$ add $r=3$ OR $r-8=5\longrightarrow$ add 8 to each side $r-8+8=5+8\longrightarrow$ add $r=13$

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