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In each of the following exercises, solve the given inequality.$$x^{3}-16 x<0$$

$x<-4$ or $0<x<4$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Campbell University

McMaster University

Idaho State University

Lectures

03:58

In each of the following e…

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02:55

00:48

Solve each polynomial ineq…

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Well, hello there, everybody. We've got a question here. X cubed minus 16 is greater than zero. Excuse me. That's what it should be. 16 x is less than zero. First thing when I do is a factor that are X and then we know we can factor this even further. Could do eggs X minus four and then an ex us or it's less than zero. You know, we take each of our factors and we set that equal to zero. We've gotta exit poster zero. Then we have X minus four is equal to zero. We so far excellent exist before, and then X plus four is equal to zero. So X is equal to negative four. We're gonna draw out a number line. You will have our infinity here negative in 30 year zero here or here. We're gonna look to satisfy out inequality by solving for values within each region. And we'll start off with a value between 400 we could choose something simple, like a five. We'll plug it in for X. All right, so we'll get one times five. It's 55 times 99 So we will get I don't know 45. Okay, that's a positive value. We know we need to get less of zero. Has to be negative. Therefore, this region is not satisfied. And these were our exports. Let's choose the value homes uniform. We'll start off with one. Keep it simple. So I have a negative three multiplied by. Excuse me, ***. Three multiplied by five, which is negative. 15. And that is definitely less than zero. So we can say, Well, that is satisfied within the three. Let's pick a value from negative four to see. Well, we could pick negative one. We have, uh, positive five multiplied by a positive threes. We get 15. We know that will not satisfy our region. Speak a value between negative for infinity. You can pick negative five. We'll get negative one multiplied by negative nine, which is 99 times 25. 45. We know that will satisfy outreach. Okay. And then when we write this out, we look at our regions. We've got one region that it's satisfied negative for infinity. He will say whatever X is less than or equal to negative four inequality satisfied. And then our second region, which is when x is greater than zero, right? It the other way. So X is greater than zero, but less than were that one should just be. This right here should just be a less than negative for and that will be our final answer. So we'll see what X is less than negative. Four and one. Life X is greater than zero, but less than four. Our inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching.

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