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In each of the following exercises, solve the given inequality.$$10 x^{2}+7 x-12<0$$

$$-3 / 2<x<4 / 5$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

Baylor University

Idaho State University

Lectures

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In each of the following e…

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For the following exercise…

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Solve each inequality.…

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Solve each equation or ine…

All right, we've got a question here. 10 X squared plus seven X minus 12. He is less thens you will, and too small to solve for the equality. And what we do first is we just try to factor it out. It makes the problem a lot simpler. So we have five X minus four, multiplied by two x plus. Alright. Next, what we're gonna do is we're gonna take each factor, set it equal to zero. So for our X, we get X is equal to 4/5. And then for our second factor, we will get access equal to negative three. We have three house here. Workers here. You want to find the region for values where or inequality does exist to support. Choose first from value between 4/5 and infinity. You can choose five. There's which is the same thing as one. And then we'll end up getting he. We'll split one. Here you end up getting a one multiplied by five, which is a positive value. That is certainly not less than zero. So we can say does not exist within that region. Take a value between three hats and 4/5 will pick something simple, like a zero wind up getting a negative four multiplied by. Oh, sorry. My theories and make it to cleaner. All right, so we'll have a negative four times three, which is negative. 12. And that does satisfy our region. This year was supposed to be a hollow, so of course, okay, hollow circles. Then we could say, Well, it does exist within this region so we can satisfy our inequality. Now, let's pick a value between negative three has an affinity. We could pick something simple, like a negative, too. So we'll get the negative 14 multiplied by a negative one, which is a positive 14, therefore does not exist within that region. And then we write out our exile you to say our ex region must be later, then negative three halfs, but less than four lifts in order to satisfy inequality. All right, well, I hope that satisfies excusing hope that clarifies the question there. And thank you so much for watching

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