Sometimes—especially on the SAT—you’ll get a math question that doesn’t ask you to solve for x (or y, or the variable in question). Instead, you might be asked to find the value of x^2, or 9x, or perhaps even (x^2)(y) [as in the case of the first blue book test]. If you see question like this, make sure you’re aware of what you actually need to find. It may be well and good to find x—but there could be an easier way. Try this, for instance:
If 5x + 2 = 18, what is the value of 10x + 4?
You certainly could solve for x in the given equation and plug that into the expression that you are calculating. The numbers, however, are not pretty. Alternatively, you might notice that there’s a relationship between what you are told and what you need:
5x + 2 = 18
10x + 4 = ?
If you double each of your components in the equation, you get the corresponding term in the expression that you’re solving for: 5x times 2 is 10x and 2 * 2 is 4. Therefore, you can multiple the entire equation by 2, to get: 10x + 4 = 36. You’re done!
This same type of equation could come up in a way that prevents you from solving for the variable:
If 5x + 2y = 18, what is the value of 10x + 4y?
Now there’s no way to solve for each variable. You must double each term to get 10x + 4y = 36.