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In each of the following exercises, solve the given inequality.$$(3 x-2)(2 x+3)<28$$

-17 / 6 < x < 2

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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In each of the following e…

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03:28

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Solve each inequality.…

All right, We've got a question here That gives us three X minus two, multiplied by a two X plus three is less than 28. Okay, so we want to get this 28 moved over to the other side. And to do that first, we're gonna expand our factor. Um, create a polynomial. So we have six x word less. Nine x minus four X minus six. Then we move over 28 overs. We'll get six x squared minus assuming plus five X minus A 28 which would give us 34. Right now, we're gonna re factor this and we could do six x for 17. We'll have a X minus two. All right, and we'll set our factors equals zero X would then be equal to negative 17/6. And then we'll do X minus two. Go to zero. So the extra people chill. Draw out a number one from infinity to excuse me. Negative. Infinity to infinity will label our X values negative 17/6 2. I'm going to solve for the region's at which our inequality is true. So we'll pick a value between two and infinity. We could take three, six times three plus 17 three minus two muscle. So we'll get 35 multiplied by one is a positive 35 when we know that is most certainly not less than zero, this region is not satisfied. Think of the region between negative 17 or six and two, so we could pick something simple, like a hero. So we would then get a 17 multiplied by negative to just negative 34. And that does satisfy our region. There, we'll pick a value between negative 17, 6 and negative infinity. We could just pick a negative 18 6, which is the same thing as negative three. So we'll get a negative wine multiplied by negative five, which is a positive five. So we know a positive value were not to satisfy the region. When we write out our X value, say whatever X is greater than negative. 17 or six and less than two or inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching

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