# How do you solve for each of the variable 9F - 3A= 22+ 4F?

Jul 23, 2015

You isolate the terms that contain the variable you're interested in on one side of the equation.

#### Explanation:

$9 F - 3 A = 22 + 4 F$

contains two variables, $F$ and $A$. In order to be able to solve this equation for one of these two variables, you simply proceed to isolate the terms that contain said variable on one side of the equation.

• solving for $A$

To solve for $A$, simply move $9 F$ on the other side of the equation (don't forget to change its sign!)

$- 3 A = 22 + 4 F - 9 F$

This is equivalent to

$- 3 A = 22 - 5 F \text{ } \textcolor{b l u e}{\left(1\right)}$

Now simply divide both sides of the equation by $- 3$ to get the value of $A$

$\frac{\cancel{- 3} A}{\cancel{- 3}} = \frac{22 - 5 F}{- 3}$

$A = \textcolor{g r e e n}{\frac{22 - 5 F}{- 3}}$

• solving for $F$

The exact same approach can be used to solve for $F$. In fact, you can use equation $\textcolor{b l u e}{\left(1\right)}$ as a starting point.

$- 3 A = 22 - 5 F$

Isolate $- 5 F$ on one side of the equation to get

$- 5 F = - 3 A - 22$

You can go ahead an divide all terms by $- 1$ to get rid of the negative signs

$5 F = 3 A + 22$

Finally, divide bith sides of the equation by $5$ to get

$\frac{\cancel{5} F}{\cancel{5}} = \frac{3 A + 22}{5}$

F = color(green)((3A + 22)/5