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: 65



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{2y+6}{3}| \lt 2\qquad $... is equivalent to ... $-2 \lt \displaystyle \frac{2y+6}{3} \lt 2\qquad $ ... multiply all parts with $3$ $-6 \lt 2y+6 \lt 6\qquad $ ... add $-6$ to all parts $-12 \lt 2y \lt 0 \qquad $ ... divide with $2$ $-6 \lt y \lt 0$ The interval borders are excluded from the interval. The solution set is $(-6,0)$
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