SOLUTION: ax+b/cx+d=2 solve for x I have no idea how to do this problem! Can you please help?

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: ax+b/cx+d=2 solve for x I have no idea how to do this problem! Can you please help?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 10763: ax+b/cx+d=2 solve for x
I have no idea how to do this problem! Can you please help?
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Again, the problem is not clear. Do you mean +%28ax%2Bb%29%2F%28cx%2Bd%29+=+2? This is my best guess.

If so, remember a%2Fb=c%2Fd which means that ad=bc?

+%28ax%2Bb%29%2F%28cx%2Bd%29+=+2%2F1 means that 1%2A%28ax+%2B+b%29+=+2%2A%28cx%2Bd%29

ax%2Bb+=+2cx+%2B+2d

Get all the x terms on one side by subtracting 2cx from each side:
ax-2cx+%2B+b+=+2cx+-2cx+%2B+2d

Get all the non-x terms on the right side by subtracting b from each side:
ax+-2cx+%2B+b-b+=+2d+-+b
ax+-+2cx+=+2d+-+b

Factor out the x, so as to get the x's all in one place:
x%28a-+2c%29+=+2d-b

Divide both sides by (a-2c):

%28x%28a-2c%29%29%2F%28a-2c%29+=+%282d-b%29%2F%28a-2c%29

R^2 at SCC