Question

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

Answer 1

Answer:

2 ≤x≤8  

Step-by-step 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