SOLUTION: Solve for x. abx-b=ax-1

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Question 257942: Solve for x.
abx-b=ax-1
Found 2 solutions by Edwin McCravy, checkley77:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x.
abx-b=ax-1

Get all the terms that have x in them on one side and
all the terms that don't have x in them on the other side:

abx-ax=b-1

Factor out x, the letter you are solving for:

x%28ab-a%29=b-1

Divide both sides by %28ab-a%29

x%28ab-a%29%2F%28ab-a%29=%28b-1%29%2F%28ab-a%29

x%28cross%28ab-a%29%29%2F%28cross%28ab-a%29%29=%28b-1%29%2F%28ab-a%29

x=%28b-1%29%2F%28ab-a%29

But you aren't finished yet because you can
factor a out of the denominator on the right:

x=%28b-1%29%2F%28a%28b-1%29%29

Then cancel:

x=%28cross%28b-1%29%29%2F%28a%28cross%28b-1%29%29%29

x=1%2Fa  

Be sure you realize that you don't get a
 because the a was in a denominator and
you must keep it in the denominator after canceling
out the %28b-1%29's by putting a 1 over it.

Edwin

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
abx-b=ax-1
abx-ax=b-1
x(ab-a)=b-1
x=(b-1)/(ab-a)
x=(b-1)/a(b-1)
x=1/a ans.
Proof:
ab(1/a)-b=a(1/a)-1
ab/a-b=a/a-1
b-b=1-1
0=0