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

Jun 2, 2015

It may be quicker to solve $\left\mid x - 1 \right\mid \le 1$ then negate the result:

$\left\mid x - 1 \right\mid \le 1$ means $- 1 \le x - 1 \le 1$

Add $1$ to all parts to get $0 \le x \le 2$

Now negate the condition to solve the original problem:

$\left\mid x - 1 \right\mid > 1$ for $x < 0$ or $x > 2$

That is $x \in \left(- \infty , 0\right) \cup \left(2 , \infty\right)$