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In each of the following exercises, solve the given inequality.$$\frac{10}{x-3} \geq 2$$

$$3<x \leq 8$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

Baylor University

Idaho State University

Lectures

03:30

In each of the following e…

03:59

03:06

03:23

01:55

Solve each inequality alge…

00:43

04:15

03:09

01:50

03:41

02:42

03:16

05:55

03:51

05:26

05:39

All right, we've got a question here. 10 over X minus three is greater than or equal to two. We want to solve the inequality. We'll take our first or denominator here. X minus three will set that equal zero we could solve for one of our exercise three here we can actually look to solve for a second X value by moving everything over to one side and having zero on the other side. So if we do that, we'll have a 10 is greater than equal to two greater than equal to two times X minus three, which would be the same thing as 10 is greater than or equal to two X minus six on then, if you subtract 10 on both sides, you would have zero is greater than or equal to two X minus 16. Divide two bites both sides. You'll get X minus eight, and then you could take that X minus eight. Set it equal to zero and you'll have your second X value to be eight. All right, then we'll take those two X values and you're gonna label them on a number line that goes from negative infinity to infinity. Three here and ate here on your value. Excuse me. When you label three here, even though you have a greater than or equal to symbol, it will be a hollow. Um, point here because you know that if you did actually put a three in for X, you would get a zero in the denominator, which would lead to an undefined function. And then for your eight, though, you could go ahead and make a solid point. And from there you're gonna choose values between these regions and see which what domain of X would satisfy the inequality. So let's pick a value between eight and Infinity. We could choose nine, the 10/9 minus three, and you'll get 10/6, which is the same thing as 166 And we know that's certainly not greater than or equal to two. So we can say that you're inequality here is not satisfied. Alright, Then you pick a value between three and eight. You could pick five. So Toby, 10 over five minus three, which is the same thing. It's five. We know that certainly greater than or equal to two. So this region is satisfied, and then Finally, a number between three and infinity. You could pick 0 10 over negative three. We know it's the same thing as negative 3.3, which is certainly not greater than or equal to two. So that's also not gonna not gonna work as our domain tracks. So we would say that X is greater than three, but less than or equal to eight. And that will satisfy you're inequality there once again, the reason why we have a lesson or equal to symbol here because you have a solid dot here and then you have a hollow dot on three. And that's exactly why you don't have that here. All right, well, I hope that clarifies the question there. Thank you so much for watching.

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