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.$$(5 x-3)(x+5) \geq 0$$

$$x \leq-5 \text { or } x \geq 3 / 5$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Oregon State University

Idaho State University

Lectures

03:36

In each of the following e…

03:51

04:23

05:55

03:31

01:16

01:23

02:40

03:11

03:17

03:57

02:25

03:43

04:05

03:07

05:45

Solve each inequality alge…

02:10

Solve the inequality. …

All right, we've got a question here, which is five x minus three multiplied by X plus five. And that's supposed to be greater than or equal to zero. Only want to solve the inequality. Start off. We take each factor and we said it equal to zero and solve for X will get three divided by five. Went to the next one, which is experts. Five because zero. So get exit was too negative. Okay, then what we do is we draw out a number line, and we place our two X values within the number line. So let's say we've got a negative five here. Does not need to be proportional at all. You just want to give yourself a visual depiction on. Then you're gonna solve for each region and determine if the that domain of X values would satisfy the inequality. So let's choose a value between 3/5 and infinity, so we could start off by choosing one. So we'll get five times one. We're just We're just gonna plug that in for our X value and we'll have a one plus five we're gonna solve. So we have five minus three with this 22 times of 5 10, we can confirm that 10 is most certainly greater than or equal to zero. So we'll say, Well, yeah, our region is satisfied within this Excuse me are inequality is satisfied within that region of X values. Now let's choose a value from negative 5 to 3/5 choose something simple like the zero. So I have zero, uh minus three and zero plus five, which is five times negative. Three is negative. 15. We know negative 15 is not greater than or equal to zero. Therefore, the region here is not satisfied. Finally, a value from negative five to negative to negative infinity. We could choose negative six, five times negative six miles. Three. The negative six plus five would give us negative 33 multiplied by a negative one, which is a positive 33. We know that it's certainly greater than zero, so we'll say well or any quality is satisfied within that region. Right now. When we write this out, we're gonna write out by saying, Well, when X is greater than or equal to 3/5 or inequality is satisfied and when X is less than or equal to negative five. Our inequality is also 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

04:28

Solve for the unknown, and then check your solution.$$13-5 x+3(2 x-9)=12…

02:49

In each of the following exercises, solve the given inequality.$$x^{2}+7…

04:12

Solve for the unknown, and then check your solution.$$7 m-4=3 m+12$$

02:32

Solve for the unknown, and then check your solution.$$x-7=9$$

Alphonse took four examinations and his average on these four exams was 83. …

01:55

In each of the following exercises, solve the given inequality.$$(x-3)(x…

00:58

Find the unknown.$$8 x^{2}-96=0$$

Find the unknown.$$\frac{3}{8}(x+7)^{2}+\frac{3}{4}=\frac{15}{2}$$

00:46

Find the unknown.$$w^{2}=-36$$

In each of the following exercises, solve the given inequality.$$(x+1)(x…