Confusion with Algebra (Substitution) I apologize for the title, I'm not sure what category this would fall under.
The advertisement read Buy $3$ tires at the regular price and get a fourth tire for only $3$ dollars. Carol paid $\$240$ for a set of $4$ tires. What is the regular price of a tire?
So I came up with $3x + 3 = 240$.
$\frac{240}{3} = 80$
$3 = 80$ does not make sense.
Why do I have to subtract the $3$ first? I was told that when using systems of equations I needed to use PEMDAS.
 A: Your mistake is that dividing by three means you divide the entire left side, so you'd end up with: $$3x+3=240,$$$$\frac{3x+3}{3}=\frac{240}{3},$$$$x+1=80,$$$$x=\$79.$$ You omitted the $3x$ term in your calculations.
A: Your goal is to manipulate your equation (which you set up correctly) to get the x by itself.  And remember that you have to do the same thing to each side of the equals sign each step along the way.  
$$3x+3=240$$
Now, you can either subtract 3 from each side or divide the entirety of each side by 3.  I see now that @onetoinfinity has posted an answer that shows how to do this, so, see if that helps...
A: PEMDAS is the order of operations for doing calculations.  Solving equations is (sort of) "undoing calculations".
For example: $10x^3-7$ means: $x$ cubed, then multiplied by $10$, then subtract $7$.  So if you are given say $x=2$ and you have to calculate this expression, you say $x=2$, so $x^3=8$, so $10x^3=80$, so $10x^3-7=73$.
But solving an equation more or less means the opposite of this: you are given the value of $10x^3-7$ and you have to find $x$.  So if you are given
$$10x^3-7=633$$
then you would add $7$ to both sides,
$$10x^3=640\ ,$$
then divide both sides by $10$,
$$x^3=64\ ,$$
then take the cube root of both sides to get $x=4$.
