(no subject)

[rivka]

In the years since high school, I've managed to completely forget how to do algebra.

No, scratch that. It's just been in the years since I took the GRE. I know I could do algebra when I took the GRE.

*sfx: tearing hair*

Comments

[redbird]

My immediate impulse is to offer assistance, but even if I weren't bleary-eyed, that's mostly a desire to prove to myself that I still remember how to do algebra.

Re:

[rivka.livejournal.com]

I understand! wcg sent me a solution, so I'm no longer in need - but I'll put the equation up for general self-assessment purposes:

x/(1-x)=y (solve for x)

Re:

[redbird]

That's one equation in two unknowns; lacking a known value for y, it's a curve.

Re:

[rivka.livejournal.com]

Right. I was looking for a general equation in which to plug different values of y, to get x.

The specific y value I was working with was 0.246, but it doesn't really matter to the construction of the general equation.

(The values of y I have are odds ratios, which I want to convert to probabilities.)

Re:

[lerryn.livejournal.com]

My solution to that is to plug in the *insert obscenity here* y value of choice, then worry about solving for x. I seem to recall the real solution invoving taking the log of both sides, but that's just a pain.

Re:

[rivka.livejournal.com]

I had the y-value-of-choice, and I still couldn't solve the goddamned equation. And I did very well on the Math GRE! It's inexplicable.

Re:

[akicif.livejournal.com]

I cheated - rearranging the equation to give things like x = y + xy didn't really help, so I tried slotting in values of 0, ±1 and ±100 for x to get the general shape of the curve. When the absolute value of x is large y tends towards -1, when x is 0 y is 0 and there's a discontinuity at x = 1, where y effectively goes from plus to minus infinity.

This, of course, didn't help solve the beastie at all, so I tried sticking it in a spreadsheet and graphing it, then zooming in to give:



It is a cheat, and there's no doubt far better software for doing it with than Excel, but when the tool I've got's a hammer....

[wcg.livejournal.com]

Hey, it doesn't have to be that complicated, really!

To solve y = x/(1-x)

First, invert: 1/y = (1-x)/x
Now rewrite the right side of the equation as 1/x - x/x
Which is 1/x - 1

So now we know that 1/y = 1/x - 1
Or, 1/y + 1 = 1/x

From there just invert again, and you end up with:

x = y/(1+y)

[akicif.livejournal.com]

<FX="slaps head" /> Of course! Forgot I could invert .... it's not just algebra I'm losing, it's basic maths.

[rivka.livejournal.com]

I forgot that I could invert, too. Unless I never knew it in the first place. Yay for wcg.

[rivka.livejournal.com]

Misha solved it in about ten seconds without inverting anything, so now I feel even more abashed. I mean, even if I did forget that you can invert, I should have been able to find this solution:

y = x/(1-x)

x = y(1-x)

x = y-yx

yx+x = y <--(this is as far as I got)

x(y+1) = y

x = y/(y+1)

Re:

[porcinea.livejournal.com]

I'd ask "where's the algebra?", but someone would probably smack me.

x / (1 - x) = y
multiply both sides by (1-x)
x = y * (1 - x)
divide both sides by y
x / y = 1 - x
divide both sides by x
1 / y = (1 - x) / x
simplify right hand side (x / x = 1)
1 / y = 1/x - 1
add 1 to both sides
1 / y + 1 = 1 / x
simplify left hand side (1 = y / y)
(1 + y ) / y = 1 / x
multiply both sides by y
1 + y = y / x
multiply both sides by x
x * (1 + y) = y
divide both sides by (1 + y)
x = y / (1 + y)

Thank you for sharing, that was pretty.

Is why I program. Breaking a problem that as a whole I can't even imagine down into wee baby steps, each v. simple. Thank you, Daisy Leland (8th grade math teacher), for bringing out the fun in function.

(This is where my math ends.)

[marykaykare.livejournal.com]

I had the exact same impulse before I remembered that I only passed algebra because the instructor so did not want me back. My brain just refuses to cope with it. So then I thought of Jordin, but I see she's already got a solution.