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In each of the following exercises, solve the given inequality.$$x^{2}+4>5$$

$x<-1$ or $x>1$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Campbell University

Oregon State University

Lectures

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In each of the following e…

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All right, we've got a question here. X squared plus four is greater than five to track four from boats. Excuse me. Track five from both sides. You want to get zero on one side, Then we're gonna go ahead and factor. This house will have X minus one and X plus one square than zero. It won't take each factor. Set it equal to zero and, uh, having a hard time with that, I'm just gonna erase it, and we draw my equal sign and then we'll have X Plus one is equal to zero. We'll have ecstasy. It's one X is equal to negative one. Okay, next thing you want to do is just draw the number line. You're gonna go from negative infinity to infinity and right out your X value. Second, calculated for who put your hollow circle because you know that it is, uh, not including those values that we don't have any equal sign there, and we're going to try to find a different values between these regions. And if those regions do satisfy the inequality that we can confirm that entire region will satisfy the quality, so speak of value between one and and you can take to I'm gonna put that in for X. So we'll get a Tu minus 111 times two plus one is three. We know three is, in fact, greater than zero. So our inequality is satisfied. There take a value between negative one and one. We can take colo. We know we'll get a negative one there. That's a negative value. So that region it's not satisfied. It's like a value between negative one negative infinity. We could pick negative too. Okay, so we'll get a negative three multiplied by negative one. Just a positive three. We know our positive value does satisfy our, um, inequality that it is greater than zero. So when we write this out, we would say, Well, this is satisfied X is less than negative one and when x is greater than that is when our inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching

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