shelley-said-that-if-x-7x-50-then-x-7-must-be-the-negative-factor-and-x-5-must-be-the-positive-facto

Question

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.

M S · Accepted Answer

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&#x27;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&#x27;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&#x27;s negative and explosive. Five is positive. So she&#x27;s going with the second possible solution here. Let&#x27;s just hope for it. So we have excess. Listen. Seven. Well, it&#x27;s a little far you next year that bought the boat. Sleds X is greater than father, so when it&#x27;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&#x27;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&#x27;s say, for example, we have a So I&#x27;m speed, you know, give us native to you can&#x27;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

Pammi Eswari · Answer

given expression is minus X squared minus seven X place five. First, we will determine the greatest common factor off the given expression. Hill G C F is one on minus one is a leading caution, so it is negative. Now. We will factor out a common factor. We do. Nick do cough Shit. Now we will express each term off the given expression as the product off opposite off the G C F. And it&#x27;s other factor. Helgi Office one on opposite off the G C F is minus one. Now we will express each term. I&#x27;m still common factor, and it&#x27;s although effect, um so the product off minus one ah exist squared is minus. X squared the product off minus one on seven x is minus seven x The product off minus one on minus five is plus file. You&#x27;re minus one is though common. Factor off. Given three terms Now we will factor out the opposite off the GC off that ISS minus one when we factor aught minus one B How x squared plus seven x minus five

Anna Steffensmeier · Answer

we were told to solve X minus five, divided by X plus seven, which is less than or equal to zero. Okay, so, off to the right hand side, you might notice that there&#x27;s this ex cannot equal negative seven. Okay, The reason that is true is because we never want our denominator. What&#x27;s in blue down here to be equal to zero, it is impossible to divide by a value of zero. So we figured out okay. If I plug in negative seven for X R denominator would go to zero. Okay, so that is why X cannot equal negative seven. Because our denominator cannot equal zero. So with this being said, we still have to solve our inequality here. So I need to figure out what values of X make this function less than or equal to zero. So I&#x27;m going to starry bye. Just figuring out, okay, I&#x27;m gonna look at what makes my top go to zero. So I&#x27;m gonna multiply by X plus seven on both sides, OK? And that will cancel out my denominator snow. I have X minus five is less than or equal to zero because zero if I multiply that throughout X and 70 times x will just give me zero and then zero times seven will still give me zero. So I have X minus five is less than or equal to zero. And so now, to get X by itself, I&#x27;m gonna add five. And X is going to be less than or equal to Fine. So we have one part of our inequality. But now we have to consider what other values could make this thing zero. Or like, where does our function stop being less than or equal to zero? That&#x27;s the question we have to ask ourselves now. And we can&#x27;t just say X is less than or equal to five. Because if he noticed appear, we have this, um uh, strength the This ex cannot equal negative seven, straining our solution. So we have toe consider this when we&#x27;re, um, trying to figure out what other values work. So let&#x27;s actually look at X being equal to negative seven. So ex equaling negative seven. If we plug that end, tow X plus seven. It&#x27;s kind of we&#x27;re considering this bit. Right? Okay. So when we have Expo seven that function there, if I have X equal to negative seven. I get a zero value can if I have X is greater the negative. Seven. What type of values come out? So what kind of values are bigger than negative? Seven? That&#x27;d be like negative six. That&#x27;d be like negative 102345 So when we have X is greater than negative seven. If I plug in any of those values like negative six, for example, negative six plus seven gives me a positive one. So when I plug in a value that&#x27;s greater than seven, I get something that&#x27;s Posy. Can&#x27;t now going Toe X is less than negative. Seven. Those are values like negative eight Negative nine negative 10 Those kinds of things. So negative eight plus seven. That gives me a negative one. So when I start to plug in values to the left of negative seven, I&#x27;m going to get something that&#x27;s negative. And so from here we have to consider okay, what kind of values that I actually want from that explosive in? Remember, In our original function, we&#x27;re looking for values that are strictly less than or equal to zero. Okay, so that means I only want to consider those kinds of values. Okay, excuse me. And so if we start with looking at those values that were less than negative seven. Let&#x27;s see what happens if I plug in negative eight for the top and the bottom of this original function. So if I plug in at X equals negative eight, plug in negative eight minus five, divided by negative eight plus seven. That would give me negative 13. Divided by negative eight plus seven is negative one. Would you do me? 13. 13 does not work for this thing because it is not less than or equal tau zero. And so we know that this doesn&#x27;t work. We already know that if I plug in zero, that doesn&#x27;t work. This means that this X is greater than negative. Seven. Has to be the other part of our solution, but let&#x27;s double check. Make sure so if I plug in negative six for X, I&#x27;m gonna get negative. Six minus five. Divided by negative six plus one, which is negative. 11 divided by but negative six plus one time in negative. Six plus seven. So negative six plus seven gives me a positive one. So negative. 11 divided by one is just a negative 11. Well, this is great. This checks out this that value is less than or equal to zero. So my solution here has to include values that are greater than negative seven, but also less than or equal to five. Okay, so those are the two things that we need here. So if I write this as one, inequality that&#x27;s going to be X is less than or equal to five. What? X is also greater than negative seven. So, in one line or in one inequality, it looks like this writing that as an interval notation, we would say Negative seven. Caramba! Five. There&#x27;s our arms are interval, But again, watching those signs, we don&#x27;t want to include that value of zero er that value of negative seven. So you&#x27;re gonna have an open bracket on the negative seven end, and we can include include that value of five. So that would be a closed bracket. And there is your answer

Khanh Ha · Answer

Hey, guys. So question is this in this factor for So what is it factor for? Why should be a product, Right? So this right here is a product for sure. So it is already factored so we don&#x27;t have to do anything else, Yeah.

Khanh Ha · Answer

Hey, guys. So question is this Russian in is factored form? No. Right. So a factored form should be a product notice. Son, This right here is a plus sign connecting to term. So? So? So So We just need to factor this rate. So what is the greatest common factor here? Five X minus one. Right, So we&#x27;ll bring it out. Okay, so the first term divided by five X minus one is three are so well right. We are here and then the second term. Don&#x27;t forget the plus sign divided by five X minus one is plus seven. So we&#x27;re right. Plus seven here. And that&#x27;s how we factory. Reach off, everyone. I&#x27;m proud of you. Thank you so much for listening.

Danielle Leedy · Answer

this problem. Where again? Being asked to factor out G c f d. Do specify that they wanted to be a negative number. When I look here, my two can&#x27;t move. I did find this by two. I&#x27;d end up with 1/2 here, so that really doesn&#x27;t do us a lot of good. However, I do know that I could get rid of some exes. So we know we need to divide each side by negative. They told us in the instructions and our smallest exponents next to the bed we&#x27;re dividing exponents. That means we&#x27;re going to subtract. So this really is going to become seven months. Five. Up here, we&#x27;ll end up with negative X to the fifth on the outside X to the fifth of reacts to the fifth battle. Cancel out. My negatives will cancel. And I&#x27;m just left with two plus. Remember this negative sign? So a negative what is seven minus five x squared? And for those of you that need it rewritten Negative X to the fifth to minus X squared. And again we could write this another way, putting on our variable first negative x squared what? Two

Problem

Write the solution set of each inequality if x is…

Problem 2 Medium Difficulty

Answer

a. Yes
b. No

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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a. Yesb. No

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Ann Xavier GantertAlgebra 2 and Trigonometry

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Algebra 2 and Trigonometry