# How do you solve and write the following in interval notation: |x-4| >2?

Oct 9, 2017

See a solution process below:

#### Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$- 2 > x - 4 > 2$

Add $\textcolor{red}{4}$ to each segment of the system of inequalities to solve for $x$ while keeping the system balanced:

$- 2 + \textcolor{red}{4} > x - 4 + \textcolor{red}{4} > 2 + \textcolor{red}{4}$

$2 > x - 0 > 6$

$2 > x > 6$

Or

$x < 2$ and $x > 6$

Or, in interval notation:

$\left(- \infty , 2\right)$ and $\left(6 , + \infty\right)$