ShmoopTube

00:03

Here's an unshmoopy question you may find on an exam somewhere in life...

00:07

Solve for x: 2 times the quantity 3x minus 6 equals negative the quantity 12 minus 6x.

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And here are the potential answers...

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OK so what is this question asking?

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Well it's just a messy "distribution and basic solve for x" equation.

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Lots of simplifyin' to be done here. As we say down on the farm.

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Let's start with the distribution part and multiply this 2 here out of the equation.

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2 times 3x is 6x, and 2 times negative 6 is negative 12. So now we have 6x minus 12.

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Do the same with the negative sign to get rid of the parentheses on the right side,

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and we get negative 12 plus 6x... or 6x minus 12.

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Both sides of the equation suddenly look uh... strikingly similar.

00:58

We have 6x minus 12 on both sides.

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If we add 12 to both sides...

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...then divide both sides by 6...

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...we get "x equals x." What does that mean? Isn't that like the ultimate "duh?"

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What it means is that to solve this equation, x can be... literally anything.

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Anything real, anyway. Like... it can't be a number divided by zero or the square

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root of a negative number or an honest politician...

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But we digress. The answer is D.

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As in, "Down on the farm."

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