ShmoopTube

00:03

One un-a-shmoopy question a-comin’ a-right up!

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The solution to the absolute value inequality… the absolute value of x minus 3 is less than 7 is… what?

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And here are the potential answers…

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So… what is this question asking?

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Ooh – we have a few things going on here – absolute value and inequalities….

00:27

We have to put numbers on either side of our variable… so we have a range for x.

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We really have 2 equations we’re solving here as with any absolute value problem…

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and we start with the rosy, positive one.

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First assume that the absolute value things don’t exist… and it’s just the quantity

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x minus 3 is less than 7.

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So we add 3 to both sides to get x is less than 10. We know 10 is on the end… and we

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can cross out A or B as potential answers.

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But now let’s think about how we solve for the LESS THAN part of the equation.

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We need to flip the little “greater than” thingy here – how do we do that?

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We multiply by a negative number – in this case… negative 1.

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So think about it as negative 1 times the quantity x minus 3… all now GREATER than 7.

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We get negative x plus 3 is greater than 7…

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Subtract 3 from both sides to get negative x is greater than 4…

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…then divide both sides by negative one to get x is greater than negative 4…

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So our answer is C.

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As in, “Claustrophobia.”

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