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In each of the following exercises, solve the given inequality.$$(5 x-3)(x+5)<0$$

$$-5<x<3 / 5$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:30

In each of the following e…

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05:55

03:51

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01:16

03:11

02:40

04:05

02:25

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03:07

03:43

00:12

Solve each inequality.…

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00:54

Solve each three-part ineq…

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03:30

All right, We've got an inequality here, which is five x minus five, multiplied by a X plus five. All of that is less than zero. And what you want to do first is just solve for our exes. By setting each factor equal to zero, we'll have X is equal to negative five or five. Would you secrets a negative one? The X five is equal to zero, so X is equal to negative five. This should. This should be a positive one. Sorry. All right, now we're going to draw out a number line. Have negative infinity on one side. I'm sorry. This should be positive. Infinity of a negative infinity here. Then we'll label our one and our negative five. And we just want to determine for what region of X values will our inequality be satisfied? So, first of all, let's choose a value from one to infinity We can choose to. So we'll say. Well, five times two minus five, multiplied by two plus five. And we're just plugging in to for our X will get a 10 minus five is five multiplied by seven is 35. We're gonna check to see if it satisfies inequality. What we could see 35 is most certainly not less than zero. Therefore, this inequality is not satisfied within that region. Okay, and then the region between negative five and one, we could just choose something simple, like zero. We have five times zero minus five and then zero plus five. So we'll get negative. Five, multiplied by five is negative. 25 one negative. I would most certainly less than zero. So we can confirm that the region between negative five and one is satisfied. Finally, a value between negative five and negative infinity. We could just choose a negative six. So we'll have negative six plus two five and then five times Negative. Six minus five. So I have negative. 30 minus five is negative. 35 negative. 35 multiplied by a negative one. It's the same thing. That's positive. 35. You've already said that, Uh, that is not greater than excuse me less than zero. So it doesn't exist within that region either. The only region it does exist between its negative 51 So we write this as saying Well, when X is greater than negative five. But less than one our inequality is satisfied, and that will be our final answer there. Well, I just realized I apologized that this should be a three here. Okay? And that kind of changes are answer a bit. So we get instead a three lifts instead of one. Here, it should be 3/5. Okay. Regardless, though, whether it's 3/5 or not, if you actually go through and plug in thes values, the same answers should come out that this region does not qualify. This region does not qualify, and only this region does. So you'll end up having here a 3/5. All right, so it'll be from negative 5 to 3. Fifth. This will be your final answer here. Hope that clarifies the question. Thank you so much watching.

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