Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

In each of the following exercises, solve the given inequality.$$\frac{(x+2)(x-1)}{x-3} \leq 0$$

$$x \leq-2 \text { or } 1 \leq x<3$$

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…

03:40

01:50

04:07

04:15

02:42

03:28

05:55

02:31

03:06

02:30

02:36

03:16

02:55

03:14

05:26

06:36

00:28

solve each inequality. (x …

All right, we've got a question here. X plus two multiplied by X minus one all over. X minus three is less than or equal to as you will. Alright, We're gonna basically solve for our values of X here. So we'll say we have we said our factors expose 2 to 0 we can solve. Our X is equal to negative to Excuse me. I mean, what do X minus one is equal to zero. We get X is equal to one, and then we have a X minus. Three is equal to zero, so X is equal to the draw. A number line here. More label. Our one hour three No negative. All right. So since the negative to negative one came from the numerator, we can make them solid points because it's including those values. But we know that since the X minus two is in the denominator, we cannot actually have a three in here because that would make it undefined. You have to then make it a hollow circle. Ah, hollow point. Right now. Let's go ahead and plug in values for our three regions. Here we have one region that is from three to negative. Infinity pick a random value four and so we'll have four as our x four plus two multiplied by four minus one, divided by four minus three and you'll get a six multiplied by three over one, which would be 18. Know that a positive value will not be greater than excuse me will not be less than zero. Therefore, this region does not qualify. Let's pick a region. Pick a value between one and three, so we could pick, too. Let's chew, then we have to minus wine. Then we have two minus three and still get four multiplied by negative one, which is negative. Four divided by a negative one, which would give us a positive four before we know that a positive value also were not way. Actually, that's not right. I'm sorry. We have a a positive four divided by a negative force. So it'll actually be a negative four. Negative, yes. So if it's a negative value, then we actually do can confirm that the region does qualify. I will pick a value between negative two and one so we could pick negative 1.5. Would you negative 1.5 plus two into 151 This one and then we have negative 15 minus three. So have negative. Five multiplied by a negative 0.25 We divide that by maybe 1.5 months. Three. So we'll get a negative five. 18th. We know that negative values are less than equal toe want. So this region does qualify. Hold on. I'm sorry. Let's go back and check. I think I may have done that wrong. That should be positive here. This is negative. This is also negative. So you have a negative or negative should give you a positive value. This is actually possible. So that means that it actually will not qualified. Yeah. Once again, the reason is because it's actually gonna end up being positive. We'll pick a value between negative two and infinity. We'll pick negative three negative three past two. Negative three minus one. Negative three minus three and you'll get negative one times in negative four, which is four divided by a negative six. We'll get a negative value and we know that negative value do satisfy or inequality This year is correct. Alright, now, finally, when we write out our domain of X we would say, Well, whenever X is less than or equal to negative two Negative to hear the inequality is satisfied. And then whenever X is greater than or equal to one, but just less than three, right, Because we have a hollow circle here. Our inequality? Yes, Satisfied. All right. And that will be our final answer there. I hope that clarifies the question. Thank you so much for watching.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:44

Determine the domain and range of the set given inExercise 7

02:34

A farmer wants to set aside a rectangular plot of land to contain 100 square…

01:45

Determine the center and radius of the given circle and sketch its graph.

02:38

Solve each of the quadratics by first completing the square. When the roots …

02:15

In each of the following, solve the given quadratic equation exactly using t…

In each of the following exercises, solve the given inequality.$$\frac{3…

01:30

Determine if the given set is a function.$s=\{(3,5),(7,2),(3,-5),(9,11)\…

04:47

02:19

(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -i…

Find the unknown.$$(3 z-4)^{2}=64$$