Answer:
2 ≤x≤8
Explanation:
||x-5|-1| less than or equal to 2
||x-5|-1| ≤2
We have two solutions, a positive and a negative. When we take the negative, we flip the inequality
|x-5|-1 ≤2 and |x-5|-1 ≥-2
Add 1 to each side
|x-5|-1+1 ≤2+1 |x-5|-1+1 ≥-2+1
|x-5|≤3 |x-5|≥-1
This is always true
They both must be true for and's so whatever we find from |x-5|≤3 is the values for x
|x-5|≤3
x-5 ≤3 x-5 ≥ -3
Add 5 to each side
x-5+5 ≤3+5 x-5+5 ≥-3+3
x≤8 and x≥2
2 ≤x≤8