Question

How do you solve and graph `abs(n+2)>=1`?

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.

`-1 >= n + 2 >= 1`

Subtract `color(red)(2)` from each segment of system of equations to solve for `n` while keeping the system balanced:

`-1 - color(red)(2) >= n + 2 - color(red)(2) >= 1 - color(red)(2)`

`-3 >= n + 0 >= -1`

`-3 >= n >= -1`

Or

`n <= -3`; `n >= -1`

Or, in interval notation:

`(-oo, -3]`; `[-1, +oo)`

To graph this we will draw a vertical lines at `-3` and `-1` on the horizontal axis.

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

We will shade to the left and right of the lines to show the intervals: