Algebra on the SAT – Tip 1

Algebra is a core subject area of the SAT math section. Master the basics and you will be well positioned for the test.  The first rule of algebra is to ALWAYS BALANCE the equation, meaning “whatever-you-do-to-one-side,” do to the other!  It is important though to not only perform the same operation to both sides of an equation, but to every term as well.

Here’s an example:  3x-7=15.  Simple, right?

Just divide both sides by 3 in order to isolate the variable (get the x on its own), and you get x-7=5.  Perform reverse PEMDAS, add 7 and we find that x=12. Ta-da, done.

But we forgot that we must divide every single TERM by 3, not just both sides of the equation.  So we really end up with x- (7/3) = 5.  Now we’ve made ourselves a fraction, something even more complicated than before, and answer is 7 1/3, or 22/3 –something very different from x=12.

In this particular example, it’d be simplest to start with reverse PEMDAS and add 7, getting 3x=22, and then divide by 3.  But remember the rule of thumb, if you’re manipulating an equation, change every term, not just one term on both sides of the equals sign.

QUICK TIP: One way to avoid careless errors and keep track of your work is to work vertically, and mark ALL YOUR WORK.  Re-copy the entire equation at each step.