# Backsolving SAT Algebra Problems

### By James Rodkey

(ACT, SAT, SSAT, English Builder, ESOL, and Latin tutor at The Edge Learning Center)

One of the most significant differences between the SAT and the math tests you take at school is that the SAT is (largely) multiple-choice. This means that the correct answer to the question is already written on the page in front of you – you just need to pick which one of the four choices it is.

This makes certain question types susceptible to what we call backsolving – checking the answers to see which one is correct rather than solving the problem yourself and hoping that you get one of the answers. This isn’t always possible, but certain question types are not only easily solved this way, but best solved this way.

Here’s an example of a common type of algebra question, some version of which appears on many past SAT exam papers:

Many students’ instinct will be to solve this equation using the fundamentals of algebra, like this:

There are several reasons not to solve the problem this way. First of all, this is fairly time-consuming, even for a straightforward quadratic equation like this one. Secondly, solving the quadratic takes several steps, each of which introduces the opportunity to make a small mistake. Thirdly, and most importantly, the answer you get when you work out the solutions (A) isn’t even the correct answer to the question!

Although the algebra suggests two solutions, you’ll notice that 2 does not actually work when you substitute it for x in the equation:

-1, however, does work:

This happens because of the square root, which imposes restrictions on the values that will satisfy the equation (remember that square roots are always positive values).

The moral of the story is that, for questions like this one, just backsolve the question instead of doing any algebra. The answer choices only give -1 and 2 as possible solutions, so try both of those and see that only -1 works. (If neither worked, that would suggest that D is the correct answer.)

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