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 - Page 186: 2


$x=\{ -20,20 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of absolute value equality to solve the given equation, $ |x|=20 .$ 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} x=-20 \\\\\text{OR}\\\\ x=20 .\end{array} If $x=-20,$ then \begin{array}{l}\require{cancel} |-20|=20 \\\\ 20=20 \text{ (TRUE)} .\end{array} If $x=20,$ then \begin{array}{l}\require{cancel} |20|=20 \\\\ 20=20 \text{ (TRUE)} .\end{array} Hence, $ x=\{ -20,20 \} .$
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