Question

||x−3|−2|≤1
solve the inequality.

Answer 1

[0,1,2,4,5,6]

Explanation:

The given inequality is-

||x-3| - 2|<=1

Therefore, -1<=( |x-3| -2) <=1

Adding 1, we get -

1<=( |x-3|) <=3

|x-3| =1

This gives x=2 or 4

|x-3|=2

This gives x=5 or 1

|x-3|=3

This gives x=6 or x=0

Since x is real number therefore all values of x lying between [0,6] except 3 will satisfy the given inequality.