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: 28

Answer

$x=\left\{ -74,224 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |0.04x-3|=5.96 ,$ is equivalent to \begin{array}{l}\require{cancel} 0.04x-3=5.96 \text{ OR } 0.04x-3=-5.96 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 0.04x-3=5.96 \\\\ 100(0.04x-3)=(5.96)100 \\\\ 4x-300=596 \\\\ 4x=596+300 \\\\ 4x=896 \\\\ x=\dfrac{896}{4} \\\\ x=224 \\\\\text{ OR }\\\\ 0.04x-3=-5.96 \\\\ 100(0.04x-3)=(-5.96)100 \\\\ 4x-300=-596 \\\\ 4x=-596+300 \\\\ 4x=-296 \\\\ x=-\dfrac{296}{4} \\\\ x=-74 .\end{array} Hence, the solutions are $ x=\left\{ -74,224 \right\} .$
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