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: 45

Answer

$\left( -4,4 \right)$
1512915726

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |x| \lt 4 ,$ use the definition of absolute value inequalities. For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$ For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ 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} -4 \lt x \lt 4 .\end{array} In interval notation, the solution set is $ \left( -4,4 \right) .$ The colored graph is the graph of the solution set.
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