Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1-9 - Cumulative Review: 7

Answer

$x=\left\{ -\dfrac{7}{2},\dfrac{9}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |2x-1|=8 ,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable in each resulting equation. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 2x-1=8 \\\\\text{OR}\\\\ 2x-1=-8 .\end{array} Using the properties of equality to isolate the variable in each equation results to \begin{array}{l}\require{cancel} 2x-1=8 \\\\ 2x=8+1 \\\\ 2x=9 \\\\ x=\dfrac{9}{2} \\\\\text{OR}\\\\ 2x-1=-8 \\\\ 2x=-8+1 \\\\ 2x=-7 \\\\ x=-\dfrac{7}{2} .\end{array} Hence, $ x=\left\{ -\dfrac{7}{2},\dfrac{9}{2} \right\} .$
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