Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 34


The solution set is $(-\displaystyle \infty,-\frac{53}{6} ]$

Work Step by Step

The idea is to isolate x on one side. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $ 18x+45 \leq 12x-8\qquad $ ... $/-45-12x $ $ 6x \leq -53\qquad $ ... $/\div 6$ (positive) $ x \displaystyle \leq -\frac{53}{6}$ The solution set is $(-\displaystyle \infty,-\frac{53}{6} ]$
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