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: 39

Answer

$-1\le h\le7$
1514093210

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |h-3|\le4 ,$ use the definition of absolute value inequality. Then use the properties of inequality to isolate the variable. 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} -4\le h-3\le4 .\end{array} Using the properties of inequality to isolate the variable results to \begin{array}{l}\require{cancel} -4+3\le h-3+3\le4+3 \\\\ -1\le h\le7 .\end{array} The graph above confirms the solution set of the inequality.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.