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

$$-4 \leq x \leq 0 \text { or } x \geq 4$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Oregon State University

Idaho State University

Lectures

04:02

In each of the following e…

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03:14

04:15

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00:48

Solve each polynomial ineq…

03:38

Solve the inequality: $x^{…

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02:45

03:16

03:13

06:15

02:30

03:07

03:41

02:11

02:28

Solve the polynomial inequ…

All right. We've got an inequality here. X Q minus 16. X is greater than or equal to zero. Okay, first things works. You can factor this out. We'll have X squared minus 16. You know, we could factor that out. What? X minus six. Minus four. That was us. This will have a X squared will have a negative or positive for acceptance. All right. So that'll be the factory ization of this. Yeah. Reason why we factors that makes it a lot simpler. Um, when we're solving for our different X values here, we'll have one x equal to zero. Will set X minus four equals your own get excess secret. Or and then we'll set X plus four is equal to zero. Exodus to negative. All right, then what we do next is we draw out a number line, give infinity to infinity, and basically what we're gonna do is we're just gonna label all of our X points that we calculated we want to determine whether our inequality is gonna be satisfied at within those regions of values. We'll start off between four and infinity will choose five. We'll have five minus four, five plus four so we'll have Ah nine multiplied by five, which is 45. And we can confirm that 45 is in fact greater than or equal to zero. So the region here is satis satisfied singly. Let's pick a value between your own or we could pick something simple like one. We have a negative three multiplied by four instant negative 12. We know that won't satisfy the region. I think a value between negative for zero. Well, let's say let's pick a negative one. We'll have negative five multiplied by negative three to the positive three just negative 15 multiplied by a negative one, which is part of 15. This is also satisfied. Finally, between negative for an infinity will pick negative five five minus four, 35 plus four to have a negative 91 supplied by a negative five, which is negative, 45 multiplied by the negative one Applause of 45 months by by negative one is negative. 45. We know that that will not satisfy the region. All right, And then finally, when we write out our value executing our X domain, we would write that our region exists. X is greater than or equal to. So you know when X is greater than or equal to negative for, but less than or equal to see. Well, okay. And that's yeah, gonna be this region here and then also on X is greater than or equal to four. Okay? Or and that will be our final answer there for the region of X values. When inequality is satisfied, I hope that clarifies the question. Thank you so much for watching.

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