Question

||x-5|-1| less than or equal to 2

Answer 1

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