## Calculus: Early Transcendentals 8th Edition

$[-4, -1]∪[1, 4]$
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$[-4, -1]∪[1, 4]$.