# How do you solve and graph -2b + 4 > -6 ?

Aug 28, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{4}$ from each side of the inequality to isolate the $b$ term while keeping the inequality balanced:

$- 2 b + 4 - \textcolor{red}{4} > - 6 - \textcolor{red}{4}$

$- 2 b + 0 > - 10$

$- 2 b > - 10$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 2}$ to solve for $b$. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\frac{- 2 b}{\textcolor{b l u e}{- 2}} \textcolor{red}{<} \frac{- 10}{\textcolor{b l u e}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} b}{\cancel{\textcolor{b l u e}{- 2}}} \textcolor{red}{<} 5$

$b < 5$

To graph this inequality we will draw a vertical line at $5$ on the horizontal axis.

The line will be a dashed line because the inequality does not contain an "or equal to" clause.

We will shade to the left of the dashed line because the inequality operator contains a "less than" operator:

graph{x < 5}