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

$$-2 \sqrt{2} \leq x \leq 2 \sqrt{2}$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

McMaster University

Harvey Mudd College

Baylor University

Lectures

02:11

In each of the following e…

03:11

Solve each inequality.…

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01:13

Solve each inequality alge…

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03:03

All right, we've got a question here. X squared minus eight is less than or equal to zero. So what we'll do is we'll just set this equal to zero and solve our X will have X squared is equal to eight. X will then be equal to a plus minus to root two. Okay, then what we're gonna do is draw out a number. Line will go from negative. Infinity to infinity. We'll have a negative to root two and a positive to to. Okay, we're gonna plug in values within this region and determine for what region of X values. This is inequality. Satisfied? So let's choose a value between two route to and infinity. We could choose three. So we'll do three squared minus eight and we'll get nine minus eight, which is one Excuse me, and we know nine is certainly. Excuse me. One is certainly not less than or equal to zero. Therefore, we can confirm that the region of values this area here will not satisfy the inequality. Also, I wanted to make clear that we would have ah point here that iss these points do satisfy but anything greater than two and route to would not satisfied. So it looks. Let's look for values between negative to route to and to root. Two. And we'll get less shoes. Zero something simple. So we'll have zero minus eight, and that would just be negative. Eight. And we know negative eight. It's certainly less than equal to zero. Therefore, you can say, Well, the values here will satisfied inequality. Now let's choose a value between negative to route to negative infinity. We could just choose negative three. So negative three Squared is the same thing as 99 Minus eight is one once again. One. It's certainly not less than zero. Therefore, this doesn't work either. So then, when we write out our X domain would say whenever X is greater than or equal to negative to root two and the lesson are able to to boot to this inequality is satisfied. All right, well, I hope that clarifies the question. Thank you so much for watching

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