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In each of the following exercises, solve the given inequality.$$\frac{(x+2)(x-1)}{x-3}>0$$

$-2<x<1$ or $x>3$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

05:39

In each of the following e…

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02:42

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04:07

02:30

02:36

01:50

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06:36

03:06

02:55

02:31

05:26

03:16

05:55

03:13

01:20

For the following exercise…

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All right, we've got a question here. X plus two multiplied by X minus one over X minus three. And that is greater than zero. And we want to solve the inequality. Start off by taking each factor, setting an equal to zero and then solving for X. It would take our number line, and we'll go from negative infinity to infinity. That a one here, three. Here. Thank you. All right. Now, if you look at your numerator, you have a negative too. So we know that that will be a solid value on the numerator. We have a positive one. That will be a solid point. But since our X minus three is in the denominator, we know that this will have to be a hollow circle. The reason why is because if you have exactly three, uh, then you would get a, um, excuse me, you would get a undefined function. And actually, I just realized that our numerator czar will actually also be hollow. The reason why they're also gonna be hollow is because we don't have unequal symbol here. Okay, so since this is not here, it's actually relevant. Whether it's in the denominator or the numerator. They're all gonna be, although, circles. All right, now we're gonna pick values between our regions here and see whether or not those regions satisfied inequality. We'll start off with the first region here, a number between three and infinity. We could pick something as simple as four. Work plus two, four minus one or minus to be You get six times three 18, divided by 1 18. Positive through 18 is going to satisfy the inequality being greater than zero. So this is, uh, pick a number between one and three. We could pick too. Two plus two tu minus one, 213 would give us a negative. Or you know that this does not satisfy. Pick a number between one and negative to weaken pig zero. We have to two times negative one over negative three and being negative two thirds over a negative. Negative. So it actually a positive two thirds if it was just satisfied here. Harder. Our pick a value between negative to an affinity with pick Negative three. All right, so we get a negative one times Negative four, which is 44 divided by negative. Six Negative. 46 Okay, we know negative value doesn't satisfy the region. If so, than X must be greater than negative. Two in less than one. Satisfied inequality and X three greater than 4 to 3. All right, and that will be our final answer there. I hope that clarifies the question. Thank you so much for watching.

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