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: 33

Answer

The solution set is $(-\displaystyle \infty,-\frac{2}{5} ]$
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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). --- $ 8x-11 \leq 3x-13\qquad $ ... $/+11-3x $ $ 8x-3x \leq - 13+11$ $ 5x \leq -2\qquad $ ... $/\div 5$ (positive) $ x \displaystyle \leq-\frac{2}{5}$ The solution set is $(-\displaystyle \infty,-\frac{2}{5} ]$
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