Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 211: 23

$v=0$ or $v=6$

$3|v-3|=9\longrightarrow$ divide each side by 3 $3|v-3|\div3=9\div3\longrightarrow$ divide $|v-3|=3\longrightarrow$ definition of absolute value $v-3=-3$ or $v-3=3\longrightarrow$ add 3 to each part $v-3+3=-3+3$ or $v-3+3=3+3\longrightarrow$ add $v=0$ or $v=6$