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: 62


$(-\displaystyle \frac{22}{3},4)$

Work Step by Step

The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$ The idea is to isolate $x$ in the middle. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain). Multiplying/dividing with a negative number inverts the order (the inequality symbols changes). --- $|3x+5| \lt 17$ is equivalent to: $-17 \lt 3x+5 \lt 17\qquad $ ... add $-5$ to all parts $-22 \lt 3x \lt 12\qquad $ ... divide with $3$ $-\displaystyle \frac{22}{3} \lt x \lt 4$ Interval borders are excluded from the interval. The solution set is $(-\displaystyle \frac{22}{3},4)$
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