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: 27

Answer

$x=\left\{ -75,175 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |0.02x-1|=2.50 ,$ is equivalent to \begin{array}{l}\require{cancel} 0.02x-1=2.50 \text{ OR } 0.02x-1=-2.50 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 0.02x-1=2.50 \\\\ 100(0.02x-1)=(2.50)100 \\\\ 2x-100=250 \\\\ 2x=250+100 \\\\ 2x=350 \\\\ x=\dfrac{350}{2} \\\\ x=175 \\\\\text{ OR }\\\\ 0.02x-1=-2.50 \\\\ 100\left(0.02x-1\right)=(-2.50)100 \\\\ 2x-100=-250 \\\\ 2x=-250+100 \\\\ 2x=-150 \\\\ x=-\dfrac{150}{2} \\\\ x=-75 .\end{array} Hence, the solutions are $ x=\left\{ -75,175 \right\} .$
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