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i wonder how genius you are heureka!i wish i was like you!

Another from Heureka.  Thank you

Thanks Heueka,

It probably was the graphical answer that was desired. I didn't even think of that.  

x=5.5 see the graph:

I like your \underbrace{}_

Heureka, I do not think that I have seen you use that before.  

Another for me to try and remember and make use of.  Thank you.

Heureka your a genius!id like to give u a thumbs up for that!

woow thank you very much :*

5x−8=3x+3 whats the x?

$$5x-8=3x+3 \quad | \quad-3x\\\\
\underbrace{5x-3x}_{2x}-8 = \underbrace{3x-3x}_{0}+3\\\\
2x-8=3\quad | \quad +8\\\\
2x\underbrace{-8+8}_{0} =3+8\\\\
2x=11\quad | \quad:2\\\\
{\not{2}x\over \not{2}} = {11 \over 2}\\\\
x={11 \over 2}\\\\
x=5.5$$

well u musn't...thats the problem... the equation has to be the same on the both sizes...

Technically you do not transer them from one side to the other.

you add or subtract or whatever from BOTH sides.

Maybe this was a trick question Rosala.

but if we dont transfer the numbers then this cant be solved!!!

WOW 

Alan are you saying i was right!   That's amazing! 

You are right Rosala this is not a question. 

Let's see if it is -8.

3c + 4 = -20.

left hand side = 3*c+4

you have to replace the c with -8

-----------------------------

left hand side

= 3*-8+4

multiply before add and pos*neg=neg so 3*-8=-24

= -24+4

Start at -24 on the number line and go 4 places in the positive direction (because you are plussing)

=-20

= right hand side   

So yes anonymous, you are correct!   VERY GOOD WORK.   

If rotations are not allowed, but reflections are, then I think Melody's formula is correct.  See the actual arrangements below for two couples and for three couples:

Thanks anonymous and hello Alan,

Yes I can instantly see the logic behind the 2*5 but I will have to think about the -1   

Who  am I trying to kid - I do not have a clue

We should hire ourselves out to make plausable multilple choice answers for these types of questions.

(Sorry that was a bit offensive - maybe just I should hire myself out.  Maybe Chris would like to help me?)

I wonder if anyone would pay us for that? 

Why is it 2*5-1?     I don't see any intrinsic logic behind the -1

Thank you anonymous but that does not leave me any the wiser. 

The equations above your posting defines that in the affirmative.

If not, then the solution is 4! Where (n-1)! Is the basic circular permutation formula and the couples are (n).

(The !? part remains the same, though).

Im sorry but this makes no sense!

Until a few years ago, the German language was a prerequisite for engineering or mathematics.

Heureka gave a good example here (and many other places on this forum) of why this was –and should still be.

Not that I want to overcomplicate things here, but, if a wife sits to the left of her husband does that count as a different arrangement from sitting to the right of him or not?

Ok.  Didn't read Melody's reply carefully enough!  Thanks for pointing this out Anonymous.

Sorry made an error it is

$$4!*((5*2)-1)=216$$

Still not sure if all of these permutations are unique.They probably are.

It is probably

$$4!*((4*2)-1)=168$$

Some of these permutations may not be unique.

In any event, if it is a swingers party, they won’t stay that way!?

The exclamation mark with the question mark is the unknown permutation arrangement of how they will end up.

If you want it integrated to find y as a function of x then: