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 2 - Equations, Inequalities, and Problem Solving - Test: Chapter 2 - Page 151: 32


$w=\{ -15,15 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3|w|-8=37 ,$ isolate first the absolute value expression. Then use the definition of an absolute value equality to solve for the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given expression is equivalent to \begin{array}{l}\require{cancel} 3|w|-8=37 \\\\ 3|w|=37+8 \\\\ 3|w|=45 \\\\ |w|=\dfrac{45}{3} \\\\ |w|=15 .\end{array} 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} w=15 \\\\\text{OR}\\\\ w=-15 .\end{array} Hence, $ w=\{ -15,15 \} .$
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