Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Chapter 1 Test - Page 134: 13


$\left( -\infty,28 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ -\dfrac{4}{7}x \gt -16 ,$ use the Distributive property and the properties of inequality to isolate the variable. 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 $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality to isolate the variable results to \begin{array}{l}\require{cancel} 7\left( -\dfrac{4}{7}x \right) \gt 7(-16) \\\\ -4x \gt -112 .\end{array} Dividing by a negative number (and consequently reversing the sign), the inequality above is equivalent to \begin{array}{l}\require{cancel} \dfrac{-4x}{-4} \lt \dfrac{-112}{-4} \\\\ x \lt 28 .\end{array} In interval notation, the solution set is $ \left( -\infty,28 \right) .$ The colored graph is the graph of the solution set.
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