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

Apr 14, 2017

(-∞, 1] u [3, ∞)

#### Explanation:

Solve the inequality first, leaving the abs value alone in one side of the equation and then $x \ge \left(1 + 2\right)$ and then as we are moving the $- 1$ to the other side of the equation we have to change the inequality sign to $\le$, leaving $x \le \left(2 - 1\right)$

$| 2 - x | - 4 \ge - 3 \implies | 2 - x | \ge 1 \implies x \ge 3 , x \le - 1$

As interval notation,

(-∞, 1] u [3, ∞)