Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises: 55

Answer

$[-4, -1]∪[1, 4]$

Work Step by Step

The inequality$ 1≤|x|≤4$ can be calculated as follows: 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$. 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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