Question

How do you graph and solve `|x + 4| <= 6`?

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.

We can solve the problem using this system of inequalities:

`-6 <= x + 4 <= 6`

`-6 - color(red)(4) <= x + 4 - color(red)(4) <= 6 - color(red)(4)`

`-10 <= x + 0 <= 2`

`-10 <= x <= 2`

Or

`x >= 10` and `x <= 2`

Or, in interval notation:

`[-10, 2]`

To graph this we will draw two vertical lines at `-10` and `2` on the horizontal axis.

The lines will be a solid line because the inequality operators contain an "or equal to" clause.

We will shade between the lines because the interval notation shows a space between the two lines: