Question

How do you solve the inequality `abs(2-x)-4>=-3` and write your answer in interval notation?

Answer 1

`(-∞, 1] u [3, ∞)`

Explanation:

Solve the inequality first, leaving the abs value alone in one side of the equation and then `x >= (1+2)` and then as we are moving the `-1` to the other side of the equation we have to change the inequality sign to `<=`, leaving `x <= (2-1)`

`|2-x| - 4 >= -3 => |2-x| >= 1 => x >= 3, x <= -1`

As interval notation,

`(-∞, 1] u [3, ∞)`