# How do you solve and graph abs(t+6)>4?

Aug 2, 2017

See a solution process below:

#### Explanation:

The absolute value function takes any negative or positive 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.

$- 4 > t + 6 > 4$

Subtract $\textcolor{red}{6}$ from each segment of the system of inequalities to solve for $t$ while keeping the equation balanced:

$- 4 - \textcolor{red}{6} > t + 6 - \textcolor{red}{6} > 4 - \textcolor{red}{6}$

$- 10 > t + 0 > - 2$

$- 10 > t > - 2$

Or

$t < - 10$ and $t > - 2$

Or, in interval notation:

$\left(- \infty , - 10\right)$ and $\left(- 2 , + 00\right)$