# How do you solve and graph abs(w-2)<2?

Oct 22, 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.

$- 2 < w - 2 < 2$

$- 2 + \textcolor{red}{2} < w - 2 + \textcolor{red}{2} < 2 + \textcolor{red}{2}$

$0 < w - 0 < 4$

$0 < w < 4$

Or

$x > 0$ and $w < 4$

Or, in interval notation:

$\left(0 , 4\right)$

To graph this we will draw two vertical lines at $0$ and $4$ on the horizontal axis.

The line will be a dashed lines because the inequality operators do not contain an "or equal to" clause.

We will shade between the two lines to capture the interval solution: