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In each of the following exercises, solve the given inequality.$$(3 x-2)(2 x+3) \geq 28$$

$$x \leq-17 / 6 \text { or } x \geq 2$$

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

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In each of the following e…

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Solve each inequality.…

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All right, we've got a question here. Three X minus two, multiplied by two X plus three is greater than or equal to 28. So we wanna move that 28 over to the other side. It's the first thing we do is we expand this factor. We subtract 28 from both sides and then we'll have six X squared plus five x minus 34. You know, we can re factor this by having a 16 x plus 17 and a X minus two it will solve for our exes here will have six X or 17 is equal to zero. We'll have X is equal to negative. 17/6. X minus two is equal to zero actually going to insanity negative, infinity to infinity and then we'll plug in. We'll label our X values. We're gonna find the region which our exile uses true. So we'll start with the region between two in infinity, you could pick three. We're just gonna plug in 34 x for six times three poor 17 multiplied by three minus two would be the same thing as 35 times. One which is a positive 35 we know that it's most certainly greater than or equal to zero. So this region is, in fact, satisfied. Pick a value between negative 17, 6 and two. We could pick something simple, like zero. We'll have negative 34. And we know that does not satisfy the weekend. Speak a value between negative 17 6 and negative affinity with the pig. Negative 18 6, which is the same thing as negative three. That will be negative. One times negative. Three negative five. Which is the same thing. It's five. We know that that does satisfy the region. Okay, so then when we plug in our ex, well, you see whenever X is less than or equal to negative 17th over six. Okay. And whenever X is greater than or equal to two, this inequality is satisfied. All right, well, I hope that clarifies the question there. Thank you so much for watching

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