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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set: 55

Answer

$\text{Set Builder Notation: } \{ x|x\lt0 \} \\\text{Interval Notation: } (-\infty,0)$
1514846856

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -9x+17\gt17-8x .$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given equation is equivalent to \begin{array}{l}\require{cancel} -9x+17\gt17-8x \\\\ -9x+8x\gt17-17 \\\\ -x\gt0 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -x\gt0 \\\\ \dfrac{-x}{-1}\gt\dfrac{0}{-1} \\\\ x\lt0 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{ x|x\lt0 \} \\\text{Interval Notation: } (-\infty,0) .\end{array}
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