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In each of the following exercises, solve the given inequality.$$6 x^{2}-x-12>0$$

$x<-4 / 3$ or $x>3 / 2$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

05:43

In each of the following e…

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Solve each inequality.…

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Complete the solution to s…

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Solve each equation or ine…

All right, We've got an inequality here. Six X squared minus X minus 12 is greater than she will, and we're gonna try to solve for this inequality. Well, let's try. When we factor the side, it will be three x minus. Plus, for two X minus three. You get a six x squared nine x nine x and then yeah, all right. That's the factory ization for our problem and what we want to do. And the reason why we factors. It just makes the problem a lot easier. We want to do is want to take each factor, set it equal to zero software X. We get a negative four with three, and then we'll take the same thing. For our second factor. We'll get a X is equal to three over to she'll have a negative four thirds. Here you have a three halfs here, infinity here and a negative. Alright, So let's choose the value within this region from three half symphony, we could choose four half, which is the same thing as to you have three times two plus four, two times two minus three. When you solved, you get a six plus four, which is 10 multiplied by one, which is positive. 10. We can confirm that positive 10 is greater than zero. Therefore, the region of values within three halfs and infinity to infinity does satisfied inequality. Ah, value between negative four thirds and three half. You could pick something simple, like zero. You just have a positive four multiplied by negative three, which is negative. 12. So that does not satisfy the inequality. Then a value from negative four thirds and negative infinity. We could choose negative too. Two times two minus three. So the negative six plus four, which is negative two. And then here you'll get a negative seven. So negative seven multiplied by 92. Positive 14. And that doesn't satisfy you. Yeah, when we write out thes, uh, answer, we would say the inequality of satisfied when excess less than negative four thirds. And when x is greater than the house. All right, well, I hope that clarifies the question there and thank you so much watching

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