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 - Page 119: 59


$x=\{ -6,-1 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |7+2x|=5 ,$ use the definition of absolute value equality. Use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 7+2x=5 \\\\\text{OR}\\\\ 7+2x=-5 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 7+2x=5 \\\\ 2x=5-7 \\\\ 2x=-2 \\\\ x=-\dfrac{2}{2} \\\\ x=-1 \\\\\text{OR}\\\\ 7+2x=-5 \\\\ 2x=-5-7 \\\\ 2x=-12 \\\\ x=-\dfrac{12}{2} \\\\ x=-6 .\end{array} Hence, $ x=\{ -6,-1 \} .$ The colored points is the graph of the solution set.
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.