Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 2 - Systems of Linear Equations and Inequalities - 2.5 Absolute Value Equations and Inequalities - 2.5 Exercises: 6

Answer

$w=\{ -22,38 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of absolute value equality to solve the given equation, $ |w-8|=30 .$ Do checking of the solution/s. $\bf{\text{Solution Details:}}$ 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} w-8=30 \\\\\text{OR}\\\\ w-8=-30 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} w-8=30 \\\\ w=30+8 \\\\ w=38 \\\\\text{OR}\\\\ w-8=-30 \\\\ w=-30+8 \\\\ w=-22 .\end{array} If $w=38,$ then \begin{array}{l}\require{cancel} |w-8|=30? \\\\ |38-8|=30? \\\\ |30|=30? \\\\ 30=30 \text{ (TRUE)} .\end{array} If $w=-22,$ then \begin{array}{l}\require{cancel} |w-8|=30? \\\\ |-22-8|=30? \\\\ |-30|=30? \\\\ 30=30 \text{ (TRUE)} .\end{array} Hence, $ w=\{ -22,38 \} .$
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