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In each of the following exercises, solve the given inequality.$$24 x^{2}+10 x-25<0$$

$$-5 / 4<x<5 / 6$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

03:27

In each of the following e…

01:56

01:23

03:07

09:00

03:31

01:16

03:43

03:18

02:25

04:32

03:51

02:40

03:13

03:26

03:12

02:11

03:30

00:48

Solve each quadratic inequ…

03:09

and all right, we've got a question here. 24 multiplied by X squared West 10 X minus 25 Lessons. We will. First thing we want to do is factor it out. Deposited 500 miles. All right, Now, we're gonna take each factor. Set it equal to as you will X is equal to 56 Do the same thing where our or X plus five, we'll get a negative 5/4, which are ourselves a number line label. Our values of X And then we're just gonna plug in values within our regions to determine the domain of our X values. All right. A value between 56 and affinity 56 And infinity is one. You could choose any value. Longest one is satisfied, and the entire region is satisfied, so we'll get six minus 511 times nine. It's nine. That's a positive value. So it's certainly were not satisfied being less than zero a value between negative 5456 We could pick zero. You have negative five times. Five with just negative. 25. This is satisfied. Okay. All right. A value between negative 5/4 and infinity. You could choose a negative eight boards, which is the same thing as negative, too. Are you gonna get a negative 17 multiplied by a negative three, which is 51? That's positive value. So it's not satisfied. All right, then we won. We write out our X um, domain, we would say, Well, X when X is greater than negative five boards. Mhm. But when it's less than 56 than our inequality will be satisfied. All right, Well, I hope that clarifies the question there. Thank you so much for watching.

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