Solving Simple Equations

Remember that when you're trying to solve an equation with one or more variables, you need to isolate the variable. Let's walk through a simple example using the same equation from above. What if we want to solve the equation in a case where $\displaystyle y=24$?

$$$\displaystyle \begin{array}{r}y=9+3x\\24=9+3x\end{array}​$

First, subtract the same number from each side of the equation to simplify the equation without changing the fact that it's an equality. In this case, we want to subtract the number that will enable us to isolate x (x is on one side of the equal sign all by itself). We can do that by subtracting 9 from each side.

$$$\displaystyle \begin{array}{l}\,24=9+3x\\-9=-9\\\,15=3x\end{array}​$

Now we can further simplify the equation by dividing both sides by 3.

$$$\displaystyle \begin{array}{l}\frac{15}{3}=\frac{3x}{3}\\5=x\end{array}​​$

Let's practice solving for x one more time. What does x equal if $\displaystyle y=12$?

$$$\displaystyle \begin{array}{l}{12=9+3x}\\-9=-9\\{3=3x}\\\frac{3}{3}=\frac{3x}{3}\\1=x\end{array}$