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Shelley said that if $(x-7)(x-5)<0,$ then $(x-7)$ must be the negative factor and $(x-5)$ must be the positive factor.a. Do you agree with Shelly? Explain why or why not.b. When the product of two factors is negative, is it always possible to tell which is the positive factor and which is the negative factor? Justify your answer.

a. Yesb. No

Algebra

Chapter 1

THE INTEGERS

Section 8

Quadratic Inequalities

The Integers

Equations and Inequalities

Polynomials

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So Shelly said, that exploit us five times X minus seven is less saying zero. So she said that Ex Money seven must be the negative factors, so it's less than zero. And then she said that X minus by must be the positive factor. So X minus five must be good with zero with this a positive factor. So whatever we have inequalities or something for any qualities, we know that you're gonna have to possible solutions. So in this case list, Stan means negative. Luna. Write that down, listing zero beings negative and to get a negative products, we must have a positive times the negatives. But we have to backers here, so we need to software the other possibility to that. This one is native and this one is positive. But I will also give us a negative negative product furnace case. Shelley says that X minus seven. It's negative and explosive. Five is positive. So she's going with the second possible solution here. Let's just hope for it. So we have excess. Listen. Seven. Well, it's a little far you next year that bought the boat. Sleds X is greater than father, so when it's gonna bind these two so that we can have one statement. So how far here in seven years X is greater than fire? So to go that way and exploitable seven. So to go that way. And the common area between the two is here, they're here. We know that the solution is correct and who could solve for the first possibility, But we would know that it is incorrect. So yes, Shelly is correct because when you saw, you can find which is a positive factor in which is a negative back there as we just failed, we also know that explain a spot cannot be negative. So excellent. A seven has been linked to factor because we switched on. We would not get a common area between the two because the signs will be put one part beat. It wants to know that Can we always tell which is the positive factor in which is the negative factor? My answer is no. Let's say, for example, we have a So I'm speed, you know, give us native to you can't prove which is negative. They could be negative or me to be negative. No, Both give us a negative answer. But we just cannot prove which back there is negative in this case

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