ShmoopTube

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Here’s your shmoop du jour, brought to you by Absolute Value.

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Putting the “abs” in “absolute.”

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| 3x squared + 2x | = 8

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What is the largest possible value for x?

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Okay, so…while x may be equal to more than one value, the only correct answer is the largest.

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Let’s keep that in mind. First, remember that,

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when solving absolute value equations, we split them into the two possibilities.

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The number under the absolute value is either positive or negative 8.

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Let’s start with 3x squared + 2x = 8. We subtract 8 from both sides, and get 3x squared + 2x – 8 = 0.

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Then, it’s just a simple matter of using the quadratic formula.

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Plugging in our values and solving...

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...we get that x can be either 4/3, or -2.

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Remember we want the largest, so -2 is out.

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The other equation is 3x squared + 2x = -8.

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We add 8 to both sides to get our quadratic.

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Then, we use the quadratic formula again to find x.

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But when we actually try to plug our numbers into the quadratic formula, we see that we’re

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trying to take the square root of -92.

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Uh, good luck with that. Turns out there is no real solution to this equation.

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And since there are no real solutions… the only possible answers

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come from solving 3x squared + 2x = 8.

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So our answer is 4/3.

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