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

$$x \leq-11 / 20 \text { or } x \geq 1$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

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All right, We've got a question here for X minus five multiplied by five X plus four. It was greater than or equal to negative nine. First thing we're gonna do is expand out this factor. We'll get this polynomial here, and then when we do this, we'll be able to move our negative nine over, then therefore, we can have a 36. Do this. I'm sorry. It should be 16 x and then there should be in negative 25 bucks. All right, so then you'll have 20 x squared minus and nine X plus 11. All right, then you can factor the south, so you have a 20 Mhm x A minus 11 X minus one. That makes sense. 20 times X 20 x times x 20 x Where we have a negative 20. This should be negative here. I'm sorry. So you'll have a positive so 20 x squared and you'll get a negative 20 X plus an 11 x will give us a negative nine x and then 11 times negative one. This negative letter. All right, now we're gonna set thes factors equal to zero solve for X, we get X is equal to negative. 11/20. Now we'll do the same thing for our X minus. One, which will give us X is equal to one. When I draw out a number line from negative infinity to infinity, it will have excessive puts. One and X is equal to negative 11 or 20. All right, we're gonna choose a value between one infinity. So we'll choose to as our X solve. We'll get 40 plus 11 is 51 times. One is 51. A positive 51 is greater than or equal to zero. So we can confirm that the values within this region are satisfied. Excuse me. Well satisfied inequality. We'll choose a value between negative 11, 20th and one. So we'll pick zero 20 times zero plus 11. I'm zero minus one is gonna be equal to 11 times negative one, which is negative. 11. And that will not satisfied inequality. Pick a value between negative 11. 20 so we could just pick negative one. So we'll do 20 times. Negative. One plus 11. Negative. One minus one. So you get a negative nine multiplied by a negative to which is a positive 18. So this is also satisfied And then when you wrote this out, you would say whenever X is less than or equal to negative 11/20 the inequality is satisfied. And when X is greater than or equal to one in quality of satisfied. 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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