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: 66



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). --- $|\displaystyle \frac{3(x-1)}{4}| \lt 6\qquad $... is equivalent to ... $-6 \lt \displaystyle \frac{3(x-1)}{4} \lt 6\qquad $ ... multiply all parts with $4$ $-24 \lt 3x-3 \lt 24\qquad $ ... add $3$ to all parts $-21 \lt 3x \lt 27\qquad $ ... divide with $3$ $-7 \lt x \lt 9$ Interval borders are excluded from the interval. The solution set is $(-7,9)$ .
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