ShmoopTube

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Here’s an unshmoopy question you’ll find on the exam somewhere you take in life...

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at some point… Good luck.

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What is the solution set for the equation…

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the absolute value of x minus 2 equals the absolute value of x plus 3?

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And here are the potential answers...

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So… what is this question asking?

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Well, since this is an absolute value calculation, let’s start by just putting the absolute

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value thingies into 4 buckets:

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(x - 2) = (x + 3)

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-(x - 2) = (x + 3)

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(x - 2) = -(x + 3),

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and -(x - 2) = -(x + 3).

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The first and last… as well as the 2nd and 3rd… equations are identical once simplified…

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…so there are actually two versions that require solving:

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x - 2 = x + 3… and -x + 2 = x + 3.

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In the first equation, the x's cancel, which results in no solution…

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…while the second becomes -2x = 1, or x equals negative one-half.

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So answer A is our guy. As in, “Absolutely fabulous.”

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