Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises: 22

Answer

The solution is $x=2$

Work Step by Step

$|3-2x|=|5-2x|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $3-2x=5-2x$ and $3-2x=-(5-2x)$ $\textbf{Solve the first equation:}$ $3-2x=5-2x$ Take $2x$ to the left side and $3$ to the right side: $-2x+2x=5-3$ $0\ne2$ False This equation has no solution. $\textbf{Solve the second equation:}$ $3-2x=-(5-2x)$ $3-2x=-5+2x$ Take $2x$ to the left side and $3$ to the right side: $-2x-2x=-5-3$ $-4x=-8$ Solve for $x$: $x=\dfrac{-8}{-4}$ $x=2$ The solution is $x=2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.