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

$$x \leq 3 / 2$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Oregon State University

Baylor University

Lectures

03:41

In each of the following e…

05:39

02:42

04:15

03:40

03:16

03:14

04:07

05:55

05:26

03:06

02:31

02:30

06:15

02:36

02:55

02:43

03:30

03:23

06:36

all right, We've got an inequality here, which is two X minus three is greater than or equal to zero. Excuse me less than or equal to zero. And we want to determine for what values of excess inequality is true. So start off. What we do is we solve for R X by setting it equal to zero. We know that would make our X equal to three halfs. Next thing what we want to do is draw a number line and we'll set our three halves on the number line. And then we're gonna write, uh, draw a solid dotted point because we know that our inequality is satisfied, satisfied at three halfs and then we're gonna look to do is determine for what regions? This inequality is satisfied for your values of X. So pick a value between three halfs and infinity. So let's say we choose four halfs, which we know is just equal to two. So we'll plug that in for X, will be two times two minus three, and we'll get a one. We could see that one is certainly not less than or equal to zero. Therefore, we can confirm that it does not exist in this region. Now let's choose the value from three halves to negative infinity. We could just choose zero for X value. So two times 000 minus three is negative. Three We know negative three most certainly is less than or equal to zero. So we can confirm that our quality does exist in this region. Okay. And what we do then and so we just write out that are ex there. Inequality is satisfied when X is less than or equal to three half. Right. That would be the region here. And we can confirm that our answer or inequality is true. X is less than equal to three. All right, well, I hope that clarifies the question there. Thanks so much for watching.

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