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In each of the following exercises, solve the given inequality.$$2 x-3>0$$

$$x>3 / 2$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Campbell University

Oregon State University

McMaster University

Baylor University

Lectures

03:40

In each of the following e…

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All right, We've got an inequality here, which is two X minus three is greater than zero, and we want to determine what are X value. What are X domain will be to satisfy this inequality. What we do here is we take two X minus three and we pretend that this is an equal sign and we saw for our X okay, so we would have to x is equal to three and then X is equal to three divided by two. Okay, next thing we do is we draw out a number line. We just place our three or two. Do it right in the middle. Will say three over to here is in the middle. You want to determine for what region of X values this inequality is true. Got to regions here. One region that goes from three halfs infinity, one region that goes from negative infinity to three house. So we're gonna pick a value within that region, for example, we could pick four over to which we know will be too. And we'll plug that in for X will be two times two minus three and that's four minus three. Goes toe one and so we'll get a one here. We can see that one is most certainly greater than zero. Therefore, we can confirm that it does exist in this region here. Okay? And once again, we're gonna have a hollow circle here because three half is not included because it says greater than it doesn't say greater than equal to. Therefore, we would make sure that we price our point on the number line. If it's just a less than or greater than symbol, you make a hollow circle. If it's a, uh less than or greater than equal greater than equal to like for example, there was a equal symbol also there. Then you would make it a solid docket, all right, But we know in this case it's just a greater than symbol. So we're gonna have a hollow circle there. Alright, then, finally we'll look to solve for this region so we'll do three halfs to negative infinity. We could just pick zero as a value in between things Region here, So would be to time zero, which is 00 minus three is negative three. We know the negative three most certainly is not going to be greater than zero. So we could say, Well, it doesn't exist in this region. Okay, so now what we're gonna do is when we write out our X values will say, Well, X when X is greater than three halfs, our inequality is satisfied. All right, That will be our final answer there. I hope that clarifies the question. Thank you so much for watching.

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