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: 78

Answer

$x=\left\{ 2,18 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |5-0.5x|=4 ,$ 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} 5-0.5x=4 \\\\\text{OR}\\\\ 5-0.5x=-4 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5-0.5x=4 \\\\ -0.5x=4-5 \\\\ -0.5x=-1 \\\\ 10(-0.5x)=10(-1) \\\\ -5x=-10 \\\\ x=\dfrac{-10}{-5} \\\\ x=2 \\\\\text{OR}\\\\ 5-0.5x=-4 \\\\ -0.5x=-4-5 \\\\ -0.5x=-9 \\\\ 10(-0.5x)=10(-9) \\\\ -5x=-90 \\\\ x=\dfrac{-90}{-5} \\\\ x=18 .\end{array} Hence, $ x=\left\{ 2,18 \right\} .$
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