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: 64


$[-\displaystyle \frac{19}{3},7]$

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). --- $|3(x-1)+2|\leq 20\qquad $... is equivalent to ... $-20\leq 3(x-1)+2\leq 20 \qquad $ ... simplify the middle $-20\leq 3x-1\leq 20\qquad $ ... add $1$ to all parts $-19\leq 3x\leq 21 \qquad $ ... divide with $3$ $-\displaystyle \frac{19}{3}\leq x\leq 7$ Interval borders are included in the interval. The solution set is $[-\displaystyle \frac{19}{3},7]$
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