Question

How do you graph and solve `|x| ≥ 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 >= x >= 2`

Or

`x <= -2` and `x >= 2`

To graph this we will draw vertical lines at `-2` and `2` on the horizontal axis.

The lines will be solid lines because the both inequality operators contains an "or equal to" clause.

We will shade to the left and right side of the line because the inequality operator contains a "less than" and "greater than" clause respectively: