## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set: 11

equivalent

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequalities, \begin{array}{l}\require{cancel} -4x-1\le15 \\\text{and}\\ -4x\le16 .\end{array} If the solutions are the same, then the given inequalities are equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the solution of the first inequality is \begin{array}{l}\require{cancel} -4x-1\le15 \\\\ -4x\le15+1 \\\\ -4x\le16 \\\\ \dfrac{-4x}{-4}\le\dfrac{16}{-4} \\\\ x\ge-4 .\end{array} Using the properties of inequality, the solution of the second inequality is \begin{array}{l}\require{cancel} -4x\le16 \\\\ \dfrac{-4x}{-4}\le\dfrac{16}{-4} \\\\ x\ge-4 .\end{array} Since the solutions of both inequalities are the same, then the given inequalities are $\text{ equivalent .}$

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