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ACT Math 2.4 Intermediate Algebra 383 Views


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Description:

ACT Math Intermediate Algebra: Drill 2, Problem 4. Solve for x.

Language:
English Language

Transcript

00:02

Here's your shmoop du jour...

00:05

Solve for x: the absolute value of 4x plus

00:08

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

00:14

And here are the potential answers...

00:18

OK so what is this question asking?

00:20

It's a pretty vanilla absolute value question.

00:24

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

00:30

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

00:36

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

00:44

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

00:49

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

00:53

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

01:00

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

01:07

absolute value of that to make it GREATER than 18.

01:10

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

01:14

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

01:20

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

01:24

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

01:35

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

01:39

negative 5 and positive 4...

01:41

...Answer: A.

01:43

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

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