# How do you solve and graph 4.7-2.1x> - 7.9?

Jul 30, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{4.7}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$- \textcolor{red}{4.7} + 4.7 - 2.1 x > - \textcolor{red}{4.7} - 7.9$

$0 - 2.1 x > - 12.6$

$- 2.1 x > - 12.6$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 2.1}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative number we must reverse the inequality operator:

$\frac{- 2.1 x}{\textcolor{b l u e}{- 2.1}} \textcolor{red}{<} \frac{- 12.6}{\textcolor{b l u e}{- 2.1}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2.1}}} x}{\cancel{\textcolor{b l u e}{- 2.1}}} \textcolor{red}{<} 6$

$x \textcolor{red}{<} 6$

The graphs for this is:

graph{x < 6 [-10, 10, -5, 5]}