# How do you solve abs(2x+7)>23?

Oct 5, 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.

$- 23 > 2 x + 7 > 23$

First, subtract $\textcolor{red}{7}$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- 23 - \textcolor{red}{7} > 2 x + 7 - \textcolor{red}{7} > 23 - \textcolor{red}{7}$

$- 30 > 2 x + 0 > 16$

$- 30 > 2 x > 16$

Now, divide each segment by $\textcolor{red}{2}$ to solve for $x$ while keeping the system balanced:

$- \frac{30}{\textcolor{red}{2}} > \frac{2 x}{\textcolor{red}{2}} > \frac{16}{\textcolor{red}{2}}$

$- 15 > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} > 8$

$- 15 > x > 8$

Or

$x < - 15$ and $x > 8$

Or, in interval notation:

$\left(- \infty , - 15\right)$ and $\left(8 , + \infty\right)$