# How do you solve |r + 3| ≥ 7 ?

Mar 25, 2018

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.

$- 7 \ge r + 3 \ge 7$

Now, subtract $\textcolor{red}{3}$ from each side of the system of inequalities to solve for $r$ while keeping the equation balanced:

$- 7 - \textcolor{red}{3} \ge r + 3 - \textcolor{red}{3} \ge 7 - \textcolor{red}{3}$

$- 10 \ge r + 0 \ge 4$

$- 10 \ge r \ge 4$

Or

$r \le - 10$; $r \ge 4$

Or, in interval notation:

$\left(- \infty , - 10\right]$; $\left[4 , + \infty\right)$