College Algebra (11th Edition)

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

Chapter 1 - Review Exercises: 84

Answer

$\left[ -\dfrac{8}{9}, \infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 11x\ge2(x-4) ,$ 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} 11x\ge2(x)+2(-4) \\\\ 11x\ge2x-8 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 11x-2x\ge-8 \\\\ 9x\ge-8 \\\\ x\ge-\dfrac{8}{9} .\end{array} Hence, the solution set is the interval $ \left[ -\dfrac{8}{9}, \infty \right) .$
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