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You look too happy. Here’s an unshmoopy question to take you down a peg…

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When solving the equation one over x minus one-half equals 3 for x,

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which of the following is the correct order of steps?

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And here are the potential answers...

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OK, so this question is just pushing us to think about patterns of problem solving…

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and it throws in some curves and freebies as well.

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Note that potential answer B asks about SUBTRACTING a half from both sides – well, since our

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one-half on the left is already negative, we wouldn’t be able to cancel it out.

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It would just be useless so we can eliminate option B right away.

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Consider just the remaining 3 – and remember that the key goal in solving any of these

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kinds of problems is to isolate x.

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If we add a half to both sides – which is the first thing we do in the other potential

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answers – the new equation looks like this:

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1 over x equals 3 plus one-half.

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So the next step is to just simplify 3 PLUS 1 half to be uh, yeah – 3 and a half.

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Note that C has you subtracting a half as the second step here – and that’s just wrong –

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we’ve ADDED a half to both sides; so you can cross out C.

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So it gets down to D versus A.

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A suggests taking the RECIPROCAL of the result whereas D asks us to take the OPPOSITE of the result.

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The… opposite of the result? Not even sure what that would be. Sounds like someone who

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just landed on our planet and is trying to fit in.

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Taking the RECIPROCAL, however, makes sense.

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Since we have 1 over x on the left side of the equation,

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we can simply flip both sides to get x on the left…

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…and one over 3 and a half on the right… which is 1 over 7 halves… or two-sevenths.

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A it is.

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As in… “Alien mathletes.”

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