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: 43

Answer

The solution set is $(-\infty, -6)$ .
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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 the same). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $ 1-\displaystyle \frac{x}{2} \gt 4\qquad $ ... $/\times 2$ $ 2-x \gt 8\qquad $ ... $/-2$ $-x \gt 6\qquad $ ... $/\times(-1)$ ... (negative: change direction) $ x \lt -6$ The solution set is $(-\infty, -6)$ .
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