The good news: the algebra tested on the SAT is pretty straightforward. The bad news: if you are not up on your basics, then you are in trouble. Below, is the one major tip that will help you solve almost any algebraic problem you encounter.
Balancing the equation
In an algebra equation, in which there is an equal sign, think of the equation in balance. If you do anything to one side you do the exact same thing to the other side. If you multiply one side by 4, you have to multiply the other side by 4. If you subtract 3 from one side, you subtract 3 from the other side.
The goal in balancing the equation is isolation. That’s right – you want to isolate x, or get x (or whatever variable happens to be in the equation) by itself. Think of the variable as the unpopular person in the room. Everyone – that is the other numbers – want to get away.
4x + 3 = 15.
To get x by itself, first subtract 3 from both sides of the equation.
4x + 3 = 15
4x = 12
Now divide both sides of the equation by 4:
4x/4 = 12/4
x = 3
Let’s try one more:
√x = 9
Notice how x has a square root sign on top of it. We want x to be all by itself. Therefore we have to get ride of the square root sign by squaring both sides:
(√x)^2 = 9^2
x = 81
By correctly isolating x by balancing the equation, you are well on you way to solving most of the algebra on the SAT!