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In each of the following exercises, solve the given inequality.$$(5-2 x)(x+4)>0$$

$$-4<x<5 / 2$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Campbell University

McMaster University

University of Michigan - Ann Arbor

Lectures

02:25

In each of the following e…

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05:55

02:55

All right, We've got the inequality here, which is five minus two X multiplied by exports for is greater than zero. First thing we do is we take each factor and set it equal to zero so we can solve for X. So we'll get a five over to. And then finally, for the last one we know that will just be equal. Thio, Negative four. Here we draw out a number line. You go from negative infinity to infinity. We'll place our X up points that we've solved for We're gonna determine for what region of X values does our inequality exist. So let's start off between five halves and in affinity. We could choose six halves, which is the same thing as three. I'm sure we're gonna plug in 34 x and solve, So we'll get five minus six, which is negative. One multiplied by a seven. It's negative. Seven. We know negative seven is most certainly not greater than zero. So this region is not satisfied. Excuse me? Choose a value between negative four and five halfs. We could choose something simple, like a zero. A lot of zero plus four multiplied by a, uh five minus two times zero. So we'll get five multiplied by four, which is positive. 20 Positive 20 is most certainly greater than zero. So the region is satisfied here. Finally, a value from negative for infinity. Negative affinity is negative. Five. We have this answer Will have a negative 15 multiplied by a negative one. Hold on, Let me see. Two times negative. Five is negative. 10 five minus a negative number is positive numbers. We have a positive 15 multiplied by a negative one. There's a negative 15 so we can confirm that it does not exist in this region as well. Actual. Finally, we'll write this out by saying, Well, when X is greater than negative four, but less than I've have our inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching

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