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In each of the following exercises, solve the given inequality.$$(4 x-5)(5 x+4)<-9$$

$$-11 / 20<x<1$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

McMaster University

Idaho State University

Lectures

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In each of the following e…

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All right, We've got a question here for X minus five multiplied by five x plus or this less than negative nine. The first thing we'll do is we'll multiply everything across here, expand our factor. And the purpose of doing this is so that we can move that nine over. We'll have zero on one side, you 20 x squared, and you'll have negative. This should be a positive. I'm sorry. So then we'll have a negative nine x in a negative 11. Yeah, that's gonna be less than zero right now. We're gonna factor this out, so we'll get won t x. We'll have X here. Minus 11 plus one, like plus minus 11. Here. First one here. I'm doing that right, guys. Let's see. No, there should be. Why this one? Okay, all right. Now we're gonna set our factors equal to, um We're gonna set our factories. You go to zero. We'll solve for X or X would be equal to negative. 11. 20 expires. One is equal to zero. X is equal to one. It will create a number line from negative infinity to infinity label, R one and R negative. 11/20 and then we wanna find whether what region satisfy it seemed inequality. So we'll choose a number between one and infinity first, so we could pick to 20 times too less 11 tu minus one. Okay, well, look, that end and we'll get 51. That's a positive value. We know that positive value of will not be greater than excuse me will not be less than zero. Therefore, we can confirm that this region is not satisfied. Pick a value between negative, um, 11/20 and one. We could pick zero. It's 11 times negative one, which is negative. 11. This region is satisfied. Pick a value between negative 11. 20. We could pick negative one. Get on positive. Nine. We know a positive nine will not satisfy this region. Or final answer would be that X must be greater than negative 11/20 or a region to satisfy the inequality. And it must be Excuse me. Ex must be greater than negative 11 or 20 but less than one 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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