Answer
$[-4, -1]∪[1, 4]$
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$[-4, -1]∪[1, 4]$.
