Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 77

Answer

$x=\left\{ 0,20 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |2-0.2x|=2 ,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ 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} 2-0.2x=2 \\\\\text{OR}\\\\ 2-0.2x=-2 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2-0.2x=2 \\\\ -0.2x=2-2 \\\\ -0.2x=0 \\\\ x=\dfrac{0}{-0.2} \\\\ x=0 \\\\\text{OR}\\\\ 2-0.2x=-2 \\\\ -0.2x=-2-2 \\\\ -0.2x=-4 \\\\ 10(-0.2x)=10(-4) \\\\ -2x=-40 \\\\ x=\dfrac{-40}{-2} \\\\ x=20 .\end{array} Hence, $ x=\left\{ 0,20 \right\} .$
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