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

$x<3$ or $x>8$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

03:00

In each of the following e…

02:30

03:23

02:42

03:18

03:12

01:50

03:31

03:41

03:40

03:36

02:36

03:06

03:09

05:39

04:15

01:23

02:58

Solve each inequality.…

01:28

For the following exercise…

All right, we've got a question here. 10 over X minus three is less than two. All right, now here. What we're gonna do is we're gonna try to look for the factors of X that will, um, and then set them equal to zero and calculate four hour. Um, excuse me, our X values. So we'll start off with one we have here, which is X minus three. And then we'll set that equal to zero, and then we'll have X is equal to three. Right now, we can actually create one more X value by just multiplying the X minus three onto both sides, and that will be a 10 is less than or equal to two X minus six. And if we subtract 10 on both sides, you have zero is less than two X minus 16 Dubai to by both sides, you get zero is less than X minus eight. Therefore, if you set X minus eight equal to zero, your next X value will be so those are gonna be two X values there going to draw out a number line that goes from infinity to negative infinity label three and eight and then you're gonna have hollow circles on those points because we only have a less than symbol, not a less than an equal to symbol. In that case, we could plug in solid points on. What we're gonna do is we're just gonna choose values in between these regions and see if the inequality is satisfied. We could start off by choosing a value between eight infinity. We could choose nine for 10/9 minus three. Is that gonna be less than two is really the question. So what you hear is 10 over six, which is over 10 or six, definitely less than two. I think it's 1.66 That's right, and that's certainly less than two. Therefore, our nine does satisfy the region here. Uh, so So we know that the values between Infinity will satisfy the inequality. Let's choose a value between three and eight. We could choose something simple, like five. I'll scroll it down a bit, so we'll choose five. So we'll do 10/5 minus three, and we'll get 10 over to which is five and we know five. It's certainly not less than two. Therefore, this region here is not satisfied pick a value between three and infinity. Negative infinity, and we could choose a zero. So you just have 10 over and over. Negative three. Which would just give us a what is 10 or three of US? 3.333 So we'll have a negative 3.333 and that is less than two you can see. It's also satisfied in that region. So when we write out our X domain, we say, Whenever X is less than three, the inequality is satisfied. And whenever X is and here X is greater than eight, inequality is also satisfied. All right. And that's gonna be our final answer. Their hope that satisfies Excuse me. Hope that clarifies the question. Thank you so much for watching.

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