Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.6 - Absolute Value Equations - Exercise Set: 22


The only solution is $0$.

Work Step by Step

$|2x-5|=|2x+5|$ $2x-5 = 2x+5$ or $2x-5 = -(2x+5)$ Solving first equation, $2x-5 = 2x+5$ Adding $-2x$ on both sides. $2x-5-2x = 2x+5-2x$ $-5 = 5$ This is false statement. So, this equation has no solution. Solving second equation, $2x-5 = -(2x+5)$ $2x-5 = -2x-5$ Adding $5$ on both sides. $2x-5+5 = -2x-5+5$ $2x = -2x$ Adding $2x$ on both sides. $2x +2x = -2x+2x$ $4x = 0$ $x = 0$ The only solution for $|2x-5|=|2x+5|$ is $0$
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