Intermediate Algebra (12th Edition)

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

Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises: 32

Answer

$\left[ -3,\infty \right)$
1512797127

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ -2(x+4)\le6x+16 ,$ use the Distributive Property and the properties of inequality. 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 Distributive Property and the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -2(x)-2(4)\le6x+16 \\\\ -2x-8\le6x+16 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -2x-6x\le16+8 \\\\ -8x\le24 .\end{array} Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to \begin{array}{l}\require{cancel} x\ge\dfrac{24}{-8} \\\\ x\ge-3 .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ \left[ -3,\infty \right) .$
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