College Algebra (11th Edition)

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

Chapter 1 - Review Exercises - Page 164: 85


$\left( -\infty,1 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ -5x-4\ge3(2x-5) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} -5x-4\ge3(2x)+3(-5) \\\\ -5x-4\ge6x-15 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -5x-6x\ge-15+4 \\\\ -11x\ge-11 .\end{array} Dividing both sides by a negative number and consequently reversing the inequality symbol results to \begin{array}{l}\require{cancel} \dfrac{-11x}{-11}\le\dfrac{-11}{-11} \\\\ x\le1 .\end{array} Hence, the solution set is the interval $ \left( -\infty,1 \right] .$
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