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In each of the following exercises, solve the given inequality.$$\frac{(x-1)(x+2)}{x-3}>1$$

$$x>3$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

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In each of the following e…

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For the following exercise…

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Solve each inequality.…

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solve each inequality. (x …

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All right, We've got a question here in inequality X minus one multiplied by X plus one. Excuse me. Plus two, divided by X minus three is greater than one. Are we gonna do is gonna solve for all of your ex values within these factors by setting them equal to zero. So we'll start off by X minus 1020 So then you have X is equal to one X plus two is equal to zero. Then you have X is equal to negative. Two X minus three is equal to zero. So that X would be equal to three. Right from there, you're gonna create a number line that goes from negative. Infinity to infinity. The label one label Negative. 21 and three. Okay, we're gonna have all hollow circles because you have just a greater than symbol there. You're gonna plug in values within these regions and see whether or not the regions will satisfy the inequality. Okay, so we'll pick a value between three and infinity. We could pick four four minus one, multiplied by four, plus two over four minus three and we'll get three multiplied by six Is 18. 18 divided by 1 18, and you could see that 18 is certainly greater than one. Therefore, this inequality etcetera. This region of X value satisfies inequality. Choose a value between 123 We could choose to. You have to minus one two plus two, tu minus three and you'll have four divided by negative one, which is negative for mhm. Right? So you have here, you can see that negative four would not be greater than or equal to one. Excuse me would not be greater than one. Therefore, you would say that this region here does not satisfied inequality. All right, let's plug in a value from one to negative two. We could choose zero. You do negative one multiplied by two over a negative three, which is the same thing as negative two or negative three, which is two thirds. That is also not greater than one. Therefore, this region is also not satisfied taking the value between negative two and negative infinity. We could choose negative three. It's a negative three minus one negative three plus two over negative three minus three and you'll get a negative four multiplied by a negative one, which just positive four and then you're gonna divide that by a negative six. We know that that is also not greater than one. Therefore, this does not work either. All right, So when you write out your final, um, X domain, you would say, Well, this inequality is satisfied when X values are greater than three. All right, And that will be your final answer. Their hope That clarifies the question. Thank you so much for watching.

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