Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 55


$[-4, -1]∪[1, 4]$

Work Step by Step

The inequality$ 1≤|x|≤4$ can be calculated as follows: As we know that if$ |x|≥a$ Then $x≤-a,x≥a$ … (1) And if$ |x|≤a$ Then $-a≤x≤a$ … (2) Now, apply equation (1) for expression$ 1≤|x|≤4$ , we get It can be written as $|x|≥1,|x|≤4$ From equation (1), we have $|x|≥1$ then$ x≤-1,x≥1$ From equation (2), we have $|x|≤4$ then$ -4≤x≤4$ Hence, the solution set is$[-4, -1]∪[1, 4]$.
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