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

See a solution process below:

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.

Or

Or, in interval notation:

To graph this we will draw two vertical lines at

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:

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To solve and graph the inequality |w - 2| < 2, you first isolate the absolute value expression and set up two cases:

- Case: (w - 2 < 2)
- Case: (w - 2 > -2)

Solve each case separately, then graph the solution set on a number line. The solution will be the intersection of the two separate solution sets from each case.

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