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In each of the following exercises, solve the given inequality.$$x^{2}-8>0$$

$$x<-2 \sqrt{2} \text { or } x>2 \sqrt{2}$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Campbell University

Harvey Mudd College

Lectures

02:16

In each of the following e…

03:13

03:03

02:45

02:56

Solve each inequality.…

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03:11

01:13

Solve each inequality alge…

00:53

All right, We've got an inequality here. X squared minus eight is greater than zero. We want to solve for the inequality and start off. What we'll do is we'll just set this equal to zero and solve for our X values. And we will get X is equal to a plus minus two route to then what we're gonna do is we're gonna draw out our number line, and we'll go from negative infinity to infinity. We'll have a 22 and a negative to label. We want to determine for what regions of X values or the domain of X. Will this inequality be satisfied? So let's make a value between two routes to and infinity. So we could start off by choosing a three three route. Excuse me. Three squared minus eight would be a nine minus eight, which is the same thing as one. And we can confirm confirm that one is greater than zero. Therefore, this ISS satisfied that regional value satisfies the inequality. Now let's choose a value between route. Uh, excuse me. Negative to root. Two and 22 We could pick something simple. Like 00 minus eight will give us negative eight, and that's certainly not greater than zero. Therefore, our region here in the middle well, not satisfied inequality. We'll pick between negative to route to a negative infinity. We could choose negative three squared minus eight is greater than zero. So we'll have a nine minus state which would be equal to which will be equal to a one. Once again, we no one is greater than zero. Therefore, this region of values does satisfy the inequality. So when we write out our domain of X values, we would say, Well, whatever X is less than negative to to this inequality of satisfied and whenever X is greater than to root two, the inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching.

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