An Easier Way to Solve Complex Variable Equations on Standardized Tests

When you are given a daunting substitution or elimination problem on the SAT or the ISEE, it can take more than its fair share of your valuable time, and put you in a serious time crunch. When it comes to multiple choice variable problems in math, there is an easier way than what you’ve been taught in school.

Because the test makers have narrowed the answer choices down to four of five options, it is often much quicker to plug in the possible answer choices, than to figure out how to set up the problem and work it out to completion. With some practice you can plug these numbers in and find your correct answer in much less time than it would take to even set up the equation.

Let’s look at an example: Find a negative value of x that satisfies the equation

[(x+1)^² – (2x + 1)]^(1/2) + 2|x| – 6 = 0

A) -5
B) -4
C) -3
D) -2
E) -1

This seems like a daunting problem at first, where you would have to solve for x in a very difficult manner. In a problem of this complexity, you will save yourself a lot of time by simply plugging in answer choices.

Let’s start with C.

[(-3 +1)^² – (-6 + 1)]^(1/2) + 2|-3 | – 6 = 0

[(-2)^² – (-5)]^(1/2) + 6 – 6 = 0

[9]^(1/2) + 6 – 6 = 0

9 – 6 ≠ 0

So it wasn’t C, let’s try B.

[(-2 +1)^² – (-4 + 1)]^(1/2) + 2|-2| – 6 = 0

[(-1)^² – (-3)]^(1/2) + 4 – 6 = 0

[4]^(1/2) + 4 – 6 = 0

6 – 6 = 0

And there you have it; answer B is your winner.

So remember, sometimes when it comes to the most complex variable equations on the SAT, you can save a lot of time by simply plugging in the answer choices and seeing what works.

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