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In each of the following exercises, solve the given inequality.$$x^{2}+x-42>0$$

$x<-7$ or $x>6$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

University of Michigan - Ann Arbor

Lectures

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In each of the following e…

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All right, We've got to Inequality here. X squared plus X minus 42 is greater than or equal to zero. And here will factor this out. But having X a positive seven on the X minus 16 Excuse me. All right, So this will be the factor of, um, this polynomial here. Okay? Now, what we're gonna do is we're gonna set it equal to zero. We'll solve for X values. So I say, Well, X is equal to negative seven, and we'll say X is equal to six. You hear? If we take the number line way, draw it a number line. We can have six labeled here, and negative seven. Here. You have infinity here. Negative. Infinity here. And basically we're doing is trying to determine what regions the X domain exists. And based on that, we can determine for what values of X or inequality would be true. So we know that it doesn't exist at seven and six, but it could potentially exist within this region. It could exist from 60 infinity, and it could exist from negative seven to negative. So what we do is we just choose random value between our regions so we'll start off between six and 30. Public seven. So to be seven plus seven multiplied by seven minus six. And we know that's gonna be 14 multiplied by one. We know 14 A is greater than zero, so we can confirm that it does exist within this region. It finally will pick a values between negative seven and six. So we'll pick zero. We have seven multiplied by negative six, which is negative. 42. You know, that's certainly not greater than zero, so we know it does not exist in this region. Finally, a value from negative seven to infinity. We'll just pick a negative eight. So negative eight plus seven negative eight minus six So you'll have a negative one multiplied by negative 14, which is a positive 14. We know that's greater than zero, so we can confirm that it does exist within this region. All right, so then, when we write out our our X domain, we would say, Well, the inequality is true when X is greater than six and the inequality is true when excess less than negative self. It's all values greater than six and all values less than seven. Sorry, Yeah, Less than seven. That's right. On De Sol. Values greater than six. Then we confirm that are inequality is true. All right, well, I hope that clarifies question there. Thank you so much. For what?

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