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: 26

Answer

$x\displaystyle \in(-\frac{1}{2},3]$

Work Step by Step

$\left|x\right|\leq 3\quad \Leftrightarrow\quad x\in[-3,3]$ (property 8 from the table 'Absolute Values and Intervals") At the same time, $x\displaystyle \gt -1/2 \quad \Leftrightarrow\quad x\in(-\frac{1}{2},\infty]$ So, x is in the intersection of these intervals (see image) $x\displaystyle \in(-\frac{1}{2},3]$
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