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In each of the following exercises, solve the given inequality.$$(3-4 x)(2-3 x) \geq 0$$

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

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Missouri State University

McMaster University

Baylor University

Lectures

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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 a question here, which is three minus four X multiplied by a to minus three. Eggs is greater than or equal to zero, and we want to solve for these inequalities. First we're going to do is take each factor, set it equal to zero solve for X, will get a 3/4 and then for our two X minus three X will get a X is equal to two thirds. And then we're gonna draw out a number line, will set it from negative infinity to infinity. And we know that two thirds is less than 34 works. We're just gonna determine the region of values for which our X domain well satisfied inequality. So we'll start off by this region will choose a value between 3. 14 infinity. So we could start off by choosing, um, a 442 which is the same thing as one. We have three minus a four times one tu minus three times one. We're just gonna solve, so wakes up. What we're doing is we're plugging in one for X and so we get three minus four is negative. One to minus negative. Tu minus three is negative one as well. So negative times, a negative with the positive. So we have a one positive one, which is certainly greater than zero. So we could say that it does exist within this region here, a value from two thirds and 3/4. We could just pick seven right to between 0.66 point 75 which is big 0.7. She wanted 3.7. Plug that into my handy dandy calculator. We'll get a negative 0.2 We know that's not greater than zero. We doesn't exist in that region and then value from two thirds and negative infinity. We could just pick something simple, like zero left to minus the three times zero multiplied by a three minus four times zero. That'll just be three times to which is six. We know six is most certainly greater than or equal to zero. So we could say, does satisfy this region. All right, And then finally, when we write our answer out, we're going to say, Well, the inequality satisfied when X is less than or equal to two thirds and when X is greater than or equal to three forts. Yeah, we're basically confirming that any values between those two numbers the inequality, it's not satisfied. All right, well, I hope that clarifies the question. And thank you so much for watching.

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