Question

Solve the inequality:

||x−3|−2|≤1

Answer 1

Explanation:

||x-3|-2|≤ 1

-1≤|x-3|-2≤1

-1+2≤|x-3|≤1+2

1≤|x-3|≤2

we break in two parts.

|x-3|≥1

so x-3≤-1

x≤3-1

x≤2 ...(1)

or x-3≥1

x≥4 ...(2)

|x-3|≤2

-2≤x-3≤2

-2+3≤x≤2+3

1≤x≤5 ...(3)

combining all three

1≤x≤2 ∪ 4≤x≤5