ShmoopTube

00:03

Here's your shmoop du jour: Take the absolute value of the full quantity

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of seven less than two times a number. That quantity equals 1.

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What could the number be?

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And here are the potential answers...

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Whoa... tricky. What are we doing here, trying to solve a riddle so a troll will let us over his bridge?

00:28

Alright, it's a bit wordy, but let's just write this out in math-ese...

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It says... take the absolute value -- that's these straight line thingies...

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It says "of"... anything "of" is gonna go inside the straight line thingies -- so

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that quantity is...

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2x minus seven.

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See how we did that? Just kinda reversed the order there.

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Then this whole absolute value thing equals 1.

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So what are the numbers that could fulfill this solution for x?

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Well, maybe we just start with the answer set they give us. Could it be A, which is

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negative 4? Well, let's try it.

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We have 2 times negative 4, which is negative 8... then we subtract 7 to get negative 15...

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which, uh... does not equal 1. At least not in the U.S. Choice A can go bye-bye.

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Alright, let's try B... 3.

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2 times 3 is 6; subtract 7 to get negative 1... but we are taking the absolute value

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here so it's... just 1.

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Yeah, 3 works. So the answer is either B or E; we'll have to try C, or 4, to be sure.

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If we plug in 4 for x we get 2 times 4, which is 8... then subtract 7, and we have 1.

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The absolute value thingy doesn't matter for positive numbers so yeah -- x equals 1 here.

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C is true as well, so the answers are both B and C or in this problem...

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...the answer is E.

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As in, "Evil troll."

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