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And here's your shmoop du jour...

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On a number line, the distance between the integers -12

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and 10 can be expressed by which of the following?

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Here are the potential answers...

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Why don't you hit pause? Try to solve it yourself first. Let's see where that gets us.

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OK, this question is really just asking about

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number lines and absolute values.

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For starters, we have to draw a little picture.

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The number line looks like this... and the -12 is here.

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The positive 10 is here...

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and you can see that there are 22 hops, skips, or jumps between the two points.

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So now we just have to figure out which of our answer choices equals 22...

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...keep in mind that those straight line bar thingies, otherwise known as absolute value symbols...

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...will take the positive value of anything inside of them.

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Let's just brute force our way through the problem...

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...and we see that A is -12 plus ten and it gets us back to only 2 skips away from the origin.

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Remember we need 22. Distance skipping, not a sprint.

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OK, B. We go 10 forward then 12 backward -- and we're only 2 skips away from the origin.

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If we apply the absolute value function, we are 2 forward of the origin instead of 2 behind

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it, but that doesn't help us either way.

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Now try C. Twelve steps back then 10 more -- then the absolute value function moves

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us 22 steps in the positive direction -- and voila -- we have our answer. Woot.

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Just to be sure we aren't missing something, check D and that's -12, which becomes positive 12.

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...but then we subtract 10 and again only get 2 skips away from the origin.

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So the answer is C. Done.

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Doesn't it feel... freeing to find the right answer?

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