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Solve for the unknown, and then check your solution.$$\frac{5}{2} z=\frac{4}{3}$$

$$8 / 15$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

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okay, we have to follow in linear equation. The Fraction 5/2 times C is equal to 4/3. So we're going to try to solve for the Unknown Sea. And this is a linear question because C is raised to the power of one, and both expressions should equal each other. So we know that addition and subtraction will undo each other and same thing multiplication and division will under each other. So this equation can be solved two different ways. First one, we could either divide both sides of the equation by five, divided by two in order to cancel out five divided by two on the left side and isolate, See. Or we could multiply both sides of the equation by the inverse of five divided by two, which is simply just to over five. So we'll do that that route instead so well multiplied by the inverse of 2 5/2, which is 2/5. So this is two or five, and then on the right side, we also have divided by five. Now we'll go down and five divided by two or 5/2 times its inverse to over five we'll cancel each other out because gonna equal toe one. So we're left with. Just see if he go to. We have 4/3 times to over five. So when it comes to fractions, we multiply across. So we multiply the top numbers together and the bottom numbers together, so there's gonna be four times two divided by five times three. So this is eight at the top. Yeah, divided by three times five with just just 15. No, again, when it comes to multiplying fractions together we multiply the top, the over its together and the bottoms together. So for over three times to over five is the same as eight over 15 or four times. Two over three times five, which is 5 15. It divided by 15. So now we can double check to see if this is correct, so we'll just plug in eight. Divided by 15. And to the original equation, we have five divided by two times. Eat over 15. This is equal to 4/3. So again with multiple across. So it's gonna be five times eight. That's equal to 40. Divided by or over two times. 15 is 30 and this is equal to 4/3. We can see that both of these numbers are divisible by 10. So 40 divided by 10 and 30 divided by 10. That's 40 divided by tennis four and then 30. Divided by 10 is three, but we have four. Divided by three or 4/3 is equal to forward. Three, Which is true. So therefore C equals eight or 15 is the correct answer.

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