Question

How do you solve `abs(x-1)>1`?

Answer 1

It may be quicker to solve `abs(x-1) <= 1` then negate the result:

`abs(x-1) <= 1` means `-1 <= x - 1 <= 1`

Add `1` to all parts to get `0 <= x <= 2`

Now negate the condition to solve the original problem:

`abs(x-1) > 1` for `x < 0` or `x > 2`

That is `x in (-oo, 0) uu (2, oo)`