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: 13


$ 0\leq z\leq 10,\qquad$ or, $ z\in [0,10]$

Work Step by Step

Use properties from the table 'Absolute Values and Intervals". Applying Property 8: $|x|\leq a\quad\Leftrightarrow\quad -a\leq x\leq a, \quad $ for a = positive number We have: $-1\displaystyle \leq\frac{z}{5}-1\leq 1\qquad $ Applying rule 1 for inequalities, add 1 to each part of the compound inequality. $0\displaystyle \leq\frac{z}{5}\leq 2\qquad $ Apply rule 3: multiply with a positive number $0\leq z\leq 10$ This is a closed interval, $[0,10]$ (see table: "Types of intervals".)
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