College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises: 60

Answer

$x=-\dfrac{7}{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |7+2x|=0 ,$ use the properties of equality to solve for $7+2x=0.$ $\bf{\text{Solution Details:}}$ Since for any $c\ge0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 7+2x=0 \\\\\text{OR}\\\\ 7+2x=-0 .\end{array} The equations above can be simplified to the single equation \begin{array}{l}\require{cancel} 7+2x=0 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2x=-7 \\\\ \dfrac{2x}{2}=-\dfrac{7}{2} \\\\ x=-\dfrac{7}{2} .\end{array}
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