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: 69

Answer

$(-\infty,-1]\cup[3,\infty)$

Work Step by Step

The solutions of $|u|\geq c $ are the numbers that satisfy $ u\leq -c $ or $ u\geq c.$ --- $|x-1| \geq 2\Rightarrow \left\{\begin{array}{ll} x-1\leq -2 & \\ or & \\ x-1 \geq 2 & \end{array}\right.$ $ \begin{array}{lllll} x-1\leq -2 & /+1 & ...or... & x-1 \geq 2 & /+1\\ x\leq-1 & & & x \geq 3 & \\ x\in(-\infty,-1] & & or & x\in[3,\infty) & \\ & & & & \end{array} $ Solution set: $(-\infty,-1]\cup[3,\infty)$
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