## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 2 - Section 2.6 - Absolute Value Equations - Exercise Set: 21

#### Answer

$z = -5/2$

#### Work Step by Step

$|X| = |Y|$ is true only if $X = Y$ OR $X = -Y$ Given $|z + 8| = |z - 3|$ either $z + 8= z - 3$ OR $z + 8= -( z - 3)$ IF $z + 8= z - 3$ subtract $z$ from each side of the equation $8 = -3$ Since this is false, there is no solution for $X = Y$ IF $z + 8= -(z - 3)$ distribute the negative on the right side $z + 8= -z + 3$ add $z$ to each side of the equation $2z + 8 = 3$ Subtract $8$ from each side of the equation $2z = -5$ divide each side of the equation by $2$ $z = -5/2$

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