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 - Page 100: 27

Answer

$\left[ 2,\infty \right)$
1512743264

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ x-2(x-4)\le3x ,$ 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} x-2(x)-2(-4)\le3x \\\\ x-2x+8\le3x \\\\ x-2x-3x\le-8 \\\\ -4x\le-8 .\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{-8}{-4} \\\\ x\ge2 .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ \left[ 2,\infty \right) .$
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