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In each of the following exercises, solve the given inequality.$$\frac{7 x}{x+3} \geq 4$$

$x<-3$ or $x \geq 4$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:51

In each of the following e…

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03:11

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Solve each inequality.…

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04:21

For the following exercise…

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Solve each inequality and …

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All right, we've got this inequality here. Seven x over X plus. The lead is greater than or equal to four. All right, so we're going to solve for our X value here in the denominator. By setting X Plus three equal to zero, we would have X is equal to negative three. And then we could go ahead and move everything on one side and set it equal to zero and solve for X again, so we would have seven X. It's greater than or equal to four times X plus three. So we have seven X is greater than or equal support X plus 12. I mean, if we minus seven extra both sides, we would have a negative three X whilst 12 we divide negative three by both sides. We would get a zero is greater than or equal to X minus four and then X is equal to X is equal to or alright, those will be our two x values there. And then what we're gonna do is draw out a number line that'll go from negative. Infinity to infinity will label our two X values negative three and four. And then here we have a greater than or equal to simple. But since our X plus three is in the denominator and we actually plugged in a negative three, we would get a zero, and that would lead to an undefined function because of zero. That denominator doesn't work will place a hollow, um, point on our negative three before before we could have a solid point there. Now we're gonna choose values between our three regions and see whether or not the those regions satisfied the inequality. So we'll pick a number between four and eight. So, for example, we choose five and we'll plug five inch. We'll have seven times five divided by five plus three. That's 35 divided by eight. We know 35 divided by eight is the same thing as 4.375 We know that is greater than or equal to four. So therefore we could say that that region is satisfied right now we can pick a value between negative three and four, so we could just pick zero. And if we had a zero in for that X there, we know that zero would certainly not be greater than equal to zero excuse me would not be greater than equal to four. So we would say that this region does not work. And then finally, we pick a value between negative three and negative infinity. We could pick negative. Um, we could pick negative force. We'll have seven times negative. Four over negative four plus three. So it's negative. 28 divided by a negative one, which is 28 in 28 is greater than or equal to four. We know what that it is. So this region also works. All right, now, when we write out our X domain, we would say that this inequality is true when X is less than negative three and when x is greater than or equal to four once again. The reason why we have this equal to symbol is because we have a solid dot here and the reason why we don't have it for three years because we have a hollow label here. All right, well, I hope that clarifies the question. And thank you so much for watching

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