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In each of the following exercises, solve the given inequality.$$(3 x+5)(4 x-7)>0$$

$x<-5 / 3$ or $x>7 / 4$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:17

In each of the following e…

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03:47

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For the following exercise…

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07:30

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02:25

04:05

05:55

00:42

Solve each linear inequali…

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03:40

All right, We've got an inequality here, which is three x minus excusing plus five multiplied by a four X minus seven. And all of that is greater than zero. And what we're gonna do first is we're just gonna use each factor and set that equal to zero and solve for R X, we'll get a negative five thirds, and then we'll do the same for next factor, which is four X minus 17, equal to zero. So we'll get X equal to seven works. Okay, We're gonna draw out a number line. E think that a little prettier and our number line will just contain are two X values 742 negative five thirds. We want to determine the region in which our X values will satisfy the inequality here. So what we do is we just pick values between our regions, which is seven ports and infinity. So we could choose eight forts, which we could say the same thing is just too. So we have three times two plus five and a four times two minus seven were just plugging it in here on, see what it comes out to be. So we're setting it equal to our X. So we get 11 here, multiplied by a one. We get a positive 11. We can confirm that. Ah, positive 11 is certainly larger than zero. Therefore, our inequality does exist within this region. Okay? And now, finally, we're gonna choose value from negative five thirds and 7/4. So we could just choose something simple, like a zero. We have three times zero plus five, four times zero minus seven, which is the same thing. It's five times negative seven, which gives us negative 35 negative. 35 is certainly not larger than zero. So that does not exist in that region. Finally, the last reason. Negative. 5. 30 to negative infinity. We could choose a negative 6th 3rd, which is the same thing as negative, too. Three times, thanks to plus five one supplied by four times. Negative. Two minus seven. You have negative six plus five, which is negative. One on the negative, one multiplied by a negative 15. We could just be a positive 15, so we can confirm that it also exists within this region. All right, then, when we write out our X values, we say, Well, the inequality is satisfied when X is less than five thirds and the inequality of satisfied on X is greater than seven points. Right, and that will be our final answer there. I hope that clarifies the question. Thank you so much for watching.

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