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r/learnmath•
MuMuMuMuMu

[High school math] Equivalence

Hi r/learnmath!

I have some rather extensive gaps in my math education, which I'm working on closing. Could you explain to me how we get from the left hand side of the equivalence to the right hand side? (ideally step by step and/or by telling me the concepts I am missing for me to look them up, though any comment helps). Thanks in advance for your time and effort. I really appreciate it.

a(1-q) +bq = (b - c)q + a

Context for the curious: Game theoretical pay-off for a 2x2 zero-sum game to calculate a pure counterstrategy.

Posted Mar 27, 2014, 11:33 AM UTC

12
monic_binomial•

I think there's a typo: the c on the right hand side should be a.

a(1-q) +bq =a-aq+bq       (distributive property)
           =bq-aq+a       (commutative property)
           =(b-a)q+a      (distributive property)
2
Youre_Government•

Well, there's no "c" on the left hand side, so just by doing algebraic manipulations, you can't. or I cant. maybe i'm just dumb.

i got it as far as

 a+q(b-a)=a+q(b-c)

but those two are obviously not equivalent, unless there's some special relationship between what a and c represent that I am not aware of. I don't actually know anything about game theory.

1