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

Dec 19, 2017

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.

$- 1 \ge n + 2 \ge 1$

Subtract $\textcolor{red}{2}$ from each segment of system of equations to solve for $n$ while keeping the system balanced:

$- 1 - \textcolor{red}{2} \ge n + 2 - \textcolor{red}{2} \ge 1 - \textcolor{red}{2}$

$- 3 \ge n + 0 \ge - 1$

$- 3 \ge n \ge - 1$

Or

$n \le - 3$; $n \ge - 1$

Or, in interval notation:

$\left(- \infty , - 3\right]$; $\left[- 1 , + \infty\right)$

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: