Question

How do you solve `abs(x-a)>b`?

Answer 1

`x>a+b`, when `b >= 0.`
`x < a-b`, when `b <0`

Explanation:

Despite that `|x-a|>=0`, b could be negative.

So, I allow negative b also.

The inequality breaks up to

`x-a > b`, giving `x > a +b`, for `x >=a to b >=0` and

`-(x-a)>b`, giving `x< a-b`, for `x <= a to b<0`