College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Review Exercises - Page 145: 25

Answer

$x=-\dfrac{5}{3}$ or $x=3$

Work Step by Step

Put all constants on the right side: \begin{align*} |2-3x|&=9-2\\ |2-3x|&=7 \end{align*} Use the rule $|a|=b \longrightarrow a=b \text{ or } a=-b$ then solve each equation to obtain: \begin{align*} 2-3x &= 7 &\text{or}& &2-3x=-7\\\\ -3x&=7-2 &\text{or}& &-3x=-7-2\\\\ -3x&=5 &\text{or}& &-3x=-9\\\\ x&=-\frac{5}{3} &\text{or}& &x=\frac{-9}{-3}\\\\ & && &x=3 \end{align*}
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