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: 38

Answer

$-7\lt x\lt7$
1514092970

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |x|\lt7 ,$ use the definition of absolute value inequality. Then graph the solution. In the graph a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to \begin{array}{l}\require{cancel} -7\lt x\lt7 .\end{array} The graph above confirms the solution set of the inequality.
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