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For the Arithmetically Inclined


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The Problem: x/4 - 4 = 3x/4 - 6

I would work it differently than the examples already given, but it should get the same answer. Like ChuckS said, you want all the variables (unknowns) on one side of the equals side, and all knowns on the other side. Any operation (+,-,/,*) done to both sides of the equation preserves the truth of the statement.

A) multiply both sides of the equation by 4, since there is a common divisor of 4 in both variable terms.

4 * (x/4 - 4) = 4 * (3x/4 - 6) => x - 16 = 3x - 24

B) subtract x from both sides of the equation

x - 16 - x = 3x - 24 - x => -16 = 2x - 24

C) add 24 to both sides of the equation

-16 + 24 = 2x - 24 + 24 => 8 = 2x

D) divide both sides of the equation by two to determine x

8 / 2 = 2x / 2 => 4 = x

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