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SAT Math 9.6 Algebra and Functions 275 Views


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SAT Math 9.6 Algebra and Functions

Language:
English Language

Transcript

00:03

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

00:07

Putting the “abs” in “absolute.”

00:10

| 3x squared + 2x | = 8

00:15

What is the largest possible value for x?

00:20

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

00:26

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

00:29

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

00:33

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

00:37

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

00:46

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

00:49

Plugging in our values and solving...

00:57

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

01:01

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

01:05

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

01:09

We add 8 to both sides to get our quadratic.

01:12

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

01:16

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

01:20

trying to take the square root of -92.

01:23

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

01:27

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

01:30

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

01:33

So our answer is 4/3.

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