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$[-4, -1]∪[1, 4]$.
