Question

How do you graph and solve `|x| <5`?

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.

`-5 < x < 5`

Or

`x > -5` and `x < 5`

Or, in interval notation:

`(-5, 5)`

To graph this inequality we will draw two vertical lines at points `-5` and `5` on the horizontal axis.

Each line will be a dashed line because there is not an "or equal to" class in either inequality and therefore the line is not part of the solution set.

We will shade the space between the two lines.