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

$$x \leq-3 / 2 \text { or } x \geq 4 / 5$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

McMaster University

Idaho State University

Lectures

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In each of the following e…

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Solve the inequality. …

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In Problems $7-22,$ solve …

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Solve the inequality.$…

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For the following exercise…

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Solve each inequality.…

Well, hello there, everybody. You've got a question here. 10 times X squared plus seven X minus 12 is greater than equal to zero. First thing we want to do is factor this out, so we'll have a five x, the two X and then we'll try to solve for this, We could pick three and a negative work. Yes. So we get a 10 x squared, get a 15 x minus and eight X minus 12. Which gives us that in the end, so we can confirm that are factor. The accusation was done. Correct. All right. And the reason why we wanted factors, it just makes the problem a lot simpler. Take each factor and we set it equal to zero, and we will solve for X values here. We're gonna get three halfs and forth ifs. We draw ourselves a nice number line, and we're just gonna plug in our values of X that we calculated for onto this number line. We're looking to calculate the region of X values that will satisfy inequality. So we start off by choosing a value between 4/5 infinity. We could choose 5/5 which is the same thing as one. I'm just gonna plug that in for X. Then we solved. We get five minus four is one multiplied by a five is a positive five which does satisfy the inequality greater than or equal to zero, you could say Well, yes, it does exist within this region. Take a value between negative three house and forth. If we can pick something simple like a well, so you get negative four times three is negative. 12. We know that does not satisfy the region. Finally, a value between negative three house and negative infinity. We could pick something simple, like a negative, too going to solve here. We'll get a negative 14 and multiplied by a negative one, which is a positive 14. So we can confirm that it does exist within this reach. Right now, when we write out our X values or X domain here, we're going to say, Well, the inequality exists when excess snr equal to negative three halves and when X is greater than four gifts. All right, and that will be our final answer there. I hope that clarifies the question. Thank you so much for watching

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