Question

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

Answer 1

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 + color(red)(2) < w - 2 + color(red)(2) < 2 + color(red)(2)`

`0 < w - 0 < 4`

`0 < w < 4`

Or

`x > 0` and `w < 4`

Or, in interval notation:

`(0, 4)`

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: