# Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises: 27

$y=0$ or $y=3$

#### Work Step by Step

$4|2y-3|-1=11\longrightarrow$ add 1 to each side $4|2y-3|-1+1=11+1\longrightarrow$ add $4|2y-3|=12\longrightarrow$ divide each side by 4 $4|2y-3|\div4=12\div4\longrightarrow$ divide $|2y-3|=3\longrightarrow$ definition of absolute value $2y-3=-3$ or $2y-3=3$ solve each equation $2y-3=-3\longrightarrow$ add 3 to each side $2y-3+3=-3+3\longrightarrow$ add $2y=0\longrightarrow$ divide each side by 2 $2y\div2=0\div2\longrightarrow$ divide $y=0$ OR $2y-3=3\longrightarrow$ add 3 to each side $2y-3+3=3+3\longrightarrow$ add $2y=6\longrightarrow$ divide each side by 2 $2y\div2=6\div2\longrightarrow$ divide $y=3$

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