# How do you solve |4x + 9| >45?

Oct 22, 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.

$- 45 > 4 x + 9 > 45$

First, subtract $\textcolor{red}{9}$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- 45 - \textcolor{red}{9} > 4 x + 9 - \textcolor{red}{9} > 45 - \textcolor{red}{9}$

$- 54 > 4 x + 0 > 36$

$- 54 > 4 x > 36$

Now, divide each segment by $\textcolor{red}{4}$ to solve for $x$ while keeping the system balanced:

$- \frac{54}{\textcolor{red}{4}} > \frac{4 x}{\textcolor{red}{4}} > \frac{36}{\textcolor{red}{4}}$

$\frac{2 \times - 27}{\textcolor{red}{2 \times 2}} > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} > 9$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times - 27}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}} \times 2}} > x > 9$

$- \frac{27}{2} > x > 9$

Or

$x < - \frac{27}{2}$ and $x > 9$