ShmoopTube

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Here's your shmoop du jour...

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Solve for x: the absolute value of 4x plus

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2... minus 3... is greater than or equal to 15.

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And here are the potential answers...

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OK so what is this question asking?

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It's a pretty vanilla absolute value question.

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We can ignore the vertical lines for a moment...so we have 4x plus 2 minus 3 is greater than

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or equal to 15... or 4x minus 1 is greater than or equal to 15.

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Then... 4x is greater than or equal to 16... so x is greater than or equal to 4.

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Again, that's only if we ignore the absolute value lines.

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So now let's max out what we can do if we color... inside the lines.

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We're going to worry about the absolute value of 4x plus 2 being greater than or equal to 18...

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...so... think about what x value could make 4x plus 2 NEGATIVE 18; we'll then take the

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absolute value of that to make it GREATER than 18.

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That is, what NEGATIVE values of x would do this for us?

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Well, negative 1, 2 and 3 and 4 don't help us much, but negative 5 gets us there because

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we have 4 times negative 5, which is negative 20...

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... then add 2, and we have negative 18, but when we take the absolute value of it we're there.

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So the range that x can take to satisfy this equation is that it lives somewhere between

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negative 5 and positive 4...

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...Answer: A.

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And that's why you always have to be careful to... stay inside the lines.

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