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In each of the following exercises, solve the given inequality.$$(x-3)(x+4) \geq 0$$

$x \leq-4$ or $x \geq 3$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

McMaster University

Baylor University

Idaho State University

Lectures

03:16

In each of the following e…

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Solve each equation or ine…

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Solve each inequality.…

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All right, We've got the question here, which is X Plus four multiplied by. Sorry, it was next, minus three, multiplied by experts for and that is greater than or equal to zero We want to solve for the inequality. So what we'll do is we'll take each factor, set it equal to zero and solve for X. We'll get acceptable to three, and then we'll get X equal to negative four. What we're gonna do the next is draw a number line. Gonna label are points three negative four and we'll draw our dots there were looking to calculate For what regions? Region of values of x. Will this inequality We truce. We've got a region here, one here and then one here. So first we'll start off by choosing a value within that region. Three. Excuse me three and Infinity. So let's start off by choosing four, and we'll do four minus three for X. And then we'll have a four plus four and we're gonna solve and we'll get one. Multiplied by six by six. Sorry. By eight. What should be equal to eight and we know that a is most certainly greater than or equal to zero. Therefore, we can say, Well, this region here is satisfies inequality. All right. You could choose any random value between three and infinity. You could have chosen 10. You could have chosen 20 as long as it's between three infinity. Even if one of them satisfies it. That means the whole region and satisfied. All right, let's choose the value from three Thio Negative 4 to 3 so we could pick zero and we'll say it was zero minus three, multiplied by a zero plus four is equal to negative. Three multiplied by four, which is negative. 12. So we know that negative 12 most certainly is not greater than zero. So we would say, Well, it doesn't exist in that region. And then a value from negative for infinity. We could choose negative five. You have negative five miles. Three negative five plus four. It's the same thing as negative eight multiplied by a negative one, which is just eight. And we can confirm that are eight would be greater than their input. Zero Therefore, it does exist in this region. Okay, And now when we write this out in a statement form, we would right that inequality is true when X is greater than or equal to three for this region. And the inequality is also true when X is less than or equal to negative four. All right, well, that will be our final answer there. I hope that clarifies the question. And thank you so much for watching.

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