## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 2 - Cumulative Review: 45

x=4

#### Work Step by Step

We are given that $|x-3|=|5-x|$ So $x-3=5-x$ or $x-3=-(5-x)$ We can solve both of these equations for x. For $x-3=5-x$, add 3 to both sides of the equation. $x=8-x$ Add x to both sides of the equation. $2x=8$ Divide both sides of the equation by 2. $x=4$ For $x-3=-(5-x)$, use the distributive property to simplify the right side of the equation. $x-3=x-5$ Add x to both sides of the equation. $-3=-5$ This is false, so the only solution is x=4.

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