# How do you solve abs(3+d)< -4?

May 3, 2017

See the solution process below:

#### Explanation:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$4 < 3 + d < - 4$

Subtract $\textcolor{red}{3}$ from each segment of the system of equations to solve for $d$ while keeping the system balanced:

$- \textcolor{red}{3} + 4 < - \textcolor{red}{3} + 3 + d < - \textcolor{red}{3} - 4$

$1 < 0 + d < - 7$

$1 < d < - 7$

Or

$d < - 7$ and $d > 1$

Or, in interval notation:

$\left(- \infty , - 7\right)$ and $\left(1 , \infty\right)$