# How do you solve and graph |2x + 1| – 3 >6?

Aug 11, 2017

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{3}$ to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

$\left\mid 2 x + 1 \right\mid - 3 + \textcolor{red}{3} > 6 + \textcolor{red}{3}$

$\left\mid 2 x + 1 \right\mid - 0 > 9$

$\left\mid 2 x + 1 \right\mid > 9$

The absolute value function takes any number and transforms it to its non-negative form. Therefore we need to solve the term within the absolute value function for both the negative and positive value it is equated to.

$- 9 > 2 x + 1 > 9$

Next, subtract $\textcolor{red}{1}$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- 9 - \textcolor{red}{1} > 2 x + 1 - \textcolor{red}{1} > 9 - \textcolor{red}{1}$

$- 10 > 2 x + 0 > 8$

$- 10 > 2 x > 8$

Now, divide each segment by  while keeping the system balanced:color(red)(2)

$- \frac{10}{\textcolor{red}{2}} > \frac{2 x}{\textcolor{red}{2}} > \frac{8}{\textcolor{red}{2}}$

$- 5 > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} > 4$

$- 5 > x > 4$

Or

$x < - 5$ and $x > 4$

Or, in interval notation:

$\left(- \infty , - 5\right)$ and $\left(4 , + \infty\right)$