Intermediate Algebra (12th Edition)

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

Chapter 1 - Summary Exercises - Reviewing a Chapter - Solving Linear and Absolute Value Equations and Inequalities: 30

Answer

$\left( -\infty, -\dfrac{5}{2} \right]$

Work Step by Step

Using the properties of inequality, the given inequality, $ 5x-(3+x)\ge2(3x+1) ,$ simplifies to \begin{array}{l}\require{cancel} 5x-3-x\ge6x+2 \\\\ 5x-x-6x\ge2+3 \\\\ -2x\ge5 \\\\ x\le\dfrac{5}{-2} \\\\ x\le-\dfrac{5}{2} .\end{array} Hence, the solution is the interval $ \left( -\infty, -\dfrac{5}{2} \right] .$
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