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In each of the following exercises, solve the given inequality.$$\frac{x}{x-1}<\frac{3}{2}$$

$x<1$ or $x>3$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

McMaster University

Baylor University

Idaho State University

Lectures

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In each of the following e…

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For the following exercise…

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All right, we've got a question here that gives us inequality. X over X minus one is less than three halfs. All right, we can solve our X values by setting X minus one equal to zero. So we'll get X is equal to one. Then we can solve our second X value by moving everything over to one side. So we'll do. X is less than three halfs multiplied by X minus one, which would be X is less than three have X minus three house. And then if we divide excuse me. If you subtract X from both sides will get a zero is less than half X minus three halfs. Divide everything by half. You'll get a zero is less than X minus three and then you can set X minus three equals zero and solve for X is equal to three. So those would be your two X values there. Go ahead and draw out a number line. That'll go from negative infinity to infinity and we'll label it Label a one here and a three here and then we're gonna have our points. All right, now we're gonna choose values between these regions and to see if that region satisfies inequality will choose the value between three and infinity. You can choose 4. 4/4 minus one is equal to four, divided by three, which is 1.333 We know that is certainly less than a one half, which is three house thing. We can confirm that this is that this, uh, this region satisfied inequality. So choose a number between one and three. We could choose to. We'll have to over two minus one, which is equal to two and two is certainly not less than three halves. Therefore, this region does not qualify. Finally, a number between one and negative infinity. We could choose zero. You plug in a zero on that numerator there. The entire, uh, term here will go to zero. We know zero. Certainly less than three half. So therefore, this inequality is set. This region satisfies inequality. Alright. Finally, when we write out our extra main, we would say what whenever X is less than one B inequality of satisfied and whenever X is greater than three, the inequality is satisfied. All right. And that will be our final answer there. I hope that clarifies the question. Thank you for watching

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