Question

I've been brainstorming this answer for an hour now--I'm admitting temporary defeat.
If you are taking the time to answer me, please explain your logic. I really want to learn how to do this rather than getting just an answer.

Below is my nemesis.

Fill in the blank to make the expression an equivalent equation.
2-x/-x-3 = ?/x+3

Answer 1

grouping symbols would be nice

Answer 2

and really, just multiply thru by x+3 assuming thats a denominator

Answer 3

By grouping symbols I'm assuming you want it to be all put together like this\[\frac{ 2-x }{ -x-3} =\frac{ ? }{ x+3}\]

Answer 4

thats even better yes

Answer 5

Do you know how to solve this? I dont care if you dont give me the answer, If you can break it down for me I'll try to solve it myself and check my answer with you

Answer 6

i do yes

Answer 7

the thing that is messing me up is the negative in front of the x...

Answer 8

the key is in getting 'like' denominators some how.


tell me, for what multiplier, n, does: n(x+3) = -x-3 ??

Answer 9

a plain ol negative

Answer 10

yep, so, the key is to realize that the bottom on the left is just -(x+3)

move the negative to the top

Answer 11

a/-b = -a/b

Answer 12

but then my tops will be different, but maybe I'm processing wrong

Answer 13

following you so far

Answer 14

you are trying to determine a suitable top ...

\[\frac{a}{-b}=~\frac{?}{b}\]

Answer 15

\[\frac{-1}{-1}\frac{a}{-b}=~\frac{?}{b}\]
\[\frac{-a}{b}=~\frac{?}{b}\]

Answer 16

But for my homework the only part I'm allowed to change is the ? part.

Answer 17

you cant change a question mark, you are trying to solve for the question mark

Answer 18

So you are saying that eventually this will come to a point where I can insert my value for (?) ?

Answer 19

lol I hope my ? dont cancel

Answer 20

yes

there are many ways to approach a solution, the first thing i suggested was:
\[\frac{a}{-b}=~\frac{?}{b}\]
multiply thru by the b
\[\frac{a}{-b}\frac{b}{1}=~\frac{?}{b}\frac{b}{1}\]
\[a\frac{b}{-b}=~?\frac{b}{b}\]
\[a(-1)=~?(1)\]

Answer 21

the key i spose is in recognizing that -x-3 = -(x+3)

Answer 22

Give me a min to write down what I'm understanding so far

Answer 23

a whole minute ... i dont think i have that kind of time

Answer 24

I wish I had a piece of paper to write it out for you-- i'm painfully slow with the equation button

Answer 25

im adept at non equation button too

Answer 26

I am understanding that my equation can be broken in to 2-x/-(x+3) = ?/x+3
hence I need to put a - times x+3 getting an identical denominator -(x+3). Then I will need to add my other equation's top to the right one to make them equal. So I would add a 2-x to my right, but since I multiplied the bottom by a -, I need to multiply my top by the same, coming out with \[\frac{ 2-x }{ -(x+3)}=\frac{ -2+x }{ -(x+3) }\] But then wont my negatives on the top right cancel and then my answers are not equivalent?

Answer 27

you need to work the process, and let it come to the end of it on its own.

Answer 28

My big brother doesn't know how to explain this in person so don't feel bad I'm not catching on yet--thanks for taking this much time for me!

Answer 29

simplest way see this is by multiplying by some useful form of 1: -1/-1 = 1 so we dont change a thing, just the way something looks:

\[\frac{2-x}{-x-3}=\frac{k}{x+3}(\frac{-1}{-1})\]
\[\frac{2-x}{-x-3}=\frac{-k}{-x-3}\]
now, if 2 things are equal, then their parts are equal hence:

2-x = -k, multiplying both sides by -1 changes form, not value

-(2-x) = -k(-1)

-(2-x) = k = x-2

Answer 30

notice how the process is a mathical one, and we are not changing values, we are just changing the way things look to find a solution

Answer 31

Like one side being a whole apple and the other being a whole apple chopped up, same but look different

Answer 32

yes, and so we simply have to chop up one side, and sometimes glue the other, in order to make them conform to what they need to be to see that they are both the same thing

Answer 33

So, are you saying that -2+x is my answer for the ? part? Or am I missing some glue? :p

Answer 34

I probably am

Answer 35

thats the answer, the glue has dried and the final results are set

Answer 36

I had already figured that out but it didn't seem right... Are you sure?

Answer 37

(ahem, well I guess I had figured out "several" right answers) /:

Answer 38

i am sure that if:\[\frac a{-b}=\frac{k}{b}\]
then k=-a, yes

Answer 39

But isn't my answer a/-b=-k/-b ?

Answer 40

no, your answer is k=____

Answer 41

part of the process is that a/-b = -k/-b

but part of the process is not the final results, k=____ is the final result

Answer 42

I'm not getting it, sorry for taking up so much time. This is what I get for trying to tackle problems ahead of time. if you have any revelation for how to explain it further, I'd love it, but dont feel like you have to keep showing me.

Answer 43

can you tell me why you think the answer is:

a/-b = -k/-b

how does this tell us what k is equal to?

Answer 44

spose you were asked the question ... who won the game last night? but you reply with, i have to use the bathroom first.

now, is the person wanting an answer going to believe that you using the bathroom is the answer to who won the game? or are they going to wait for you to come back and finish answering the question?

Answer 45

Lucky me my chrome just kaput. Now I'm back.reading your question...

Answer 46

:)

Answer 47

Wait for me to come back.

Answer 48

lol

Answer 49

yeah, so ...

saying a/-b = -k/-b is not the answer to "what is k?" it is simply a step along the way. the answer is of the form: k=_____

Answer 50

So you are saying that k= -2+x won the game?

Answer 51

yes

Answer 52

which may need to be written as k = x-2

Answer 53

despite the negatives canceling?

Answer 54

Ohhh but then they would not cancel if you wrote it that way

Answer 55

negatives arent canceling; we are introducing negatives to change the form that the problem is in

Answer 56

some basic properties that can change form but not value are:

adding a useful form of 0
multiplying by a useful form of 1
these are called identity properties

other processess involve doing the same thing to each side of an equation, usually by making something add to 0, or divide to 1
these are called inverse properties

other than that there is a distribution process which is really just multiplication/factoring

Answer 57

n(a+b) = (a+b) + (a+b) + ... + (a+b)

(a+b) added to itself n times

as such, we have nas, and nbs that we can regroup as: na + nb

this is called distribution, and when we undistribute, we simply factor out the common n again

Answer 58

-x-3, undistributes to get us to -(x+3)

Answer 59

I plugged our answer into mathway (filled the blank spot with 2-x) to see what it said, it says "division by 0" does this confirm or deny our hypothesis?

Answer 60

What you have typed above is making a lot of sense to me.

Answer 61

the blank spot is x-2

Answer 62

oops

Answer 63

and im not sure what mathway is

Answer 64

Mathway is a site people sometimes use to double check answers

Answer 65

But I like having someone to talk to that can explain the why behind the answer

Answer 66

*cite

Answer 67

i googled the site, and this is what i get

Answer 68

since i used y in this case:

if y = 2-x then we have:


-x-3 = x+3, solving for x

-2x-3 = 3

-2x = 6

x = -3

as such, x+3 = 0 and -x-3 = 0 in which case we would have gotten a divide by zero error

Answer 69

Do you enjoy math? Is that why you help me and other people?

Answer 70

i like not being bored out of my mind ... sometimes this helps :)

Answer 71

What does your username mean? (last non math related question)

Answer 72

does it say " a mystery 64?

Answer 73

(you can probably tell I love english)

Answer 74

its just my name shortened up. back when AOL was the thing, they suggested amistre464, and i would get the same question... anthony mistretta, the 64 is just a keepsake from those old days

Answer 75

That makes sense.

Answer 76

So here is my plan--I am trusting in your answer and going with x-2 for our "glued up apple." I do understand how we came to this conclusion, but now as well as I would like. I'm going to show my big brother when he comes home and see if he can further explain it to me.

Answer 77

good luck with that plan :) my internet closes with the library so im headed home to yell at the tv and harass the nurses ...

Answer 78

Ok-Hope you are not too bored for the rest of today. Thank you for taking the time to help me out, amistre64. It meant a lot to me. Bye :)