Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Appendices - Section A.1 - Real Numbers and the Real Line - Exercises A.1 - Page AP-6: 17

Answer

$r\in(-\infty,-3]\cup[1,\infty)$
1583190240

Work Step by Step

Use properties from the table 'Absolute Values and Intervals". Applying Property $9$: $|x|\geq a\quad\Leftrightarrow\quad x\geq a\ \ $or$\ \ x\leq-a, \quad $ for a = positive number We have $\begin{array}{ll} \frac{r+1}{2}\geq 1 & /\times 2\\ r+1\geq 2 & /-1\\ r\geq 1 & \end{array}$ $\ \ $ or $\ \ $ $\begin{array}{ll} \frac{r+1}{2}\leq-1 & /\times 2\\ r+1\leq-2 & /-1\\ r\leq-3 & \end{array}$ In interval form, we can write this result as $r\in(-\infty,-3]\cup[1,\infty)$
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