# How do you solve and graph -2/3f+3<-9?

Oct 2, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the inequality to isolate the $f$ term while keeping the inequality balanced:

$- \frac{2}{3} f + 3 - \textcolor{red}{3} < - 9 - 3$

$- \frac{2}{3} f + 0 < - 12$

$- \frac{2}{3} f < - 12$

Now, multiply each side of the inequality by $\frac{\textcolor{b l u e}{3}}{\textcolor{\mathmr{and} a n \ge}{- 2}}$ to solve for $f$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality sign.

$\frac{\textcolor{b l u e}{3}}{\textcolor{\mathmr{and} a n \ge}{- 2}} \times \frac{- 2}{3} f \textcolor{red}{>} \frac{\textcolor{b l u e}{3}}{\textcolor{\mathmr{and} a n \ge}{- 2}} \times - 12$

$\frac{\cancel{\textcolor{b l u e}{3}}}{\cancel{\textcolor{\mathmr{and} a n \ge}{- 2}}} \times \frac{\textcolor{\mathmr{and} a n \ge}{\cancel{\textcolor{b l a c k}{- 2}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}} f \textcolor{red}{>} \frac{\textcolor{b l u e}{3}}{\cancel{\textcolor{\mathmr{and} a n \ge}{- 2}}} \times \textcolor{\mathmr{and} a n \ge}{\cancel{\textcolor{b l a c k}{- 12}}} 6$

$f \textcolor{red}{>} \textcolor{b l u e}{3} \times 6$

$f \textcolor{red}{>} 18$

To graph this we will draw a vertical line at $18$ on the horizontal axis.

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

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x>18 [-10, 30, -10, 10]}