Question 1043899
When you add +a to both sides, you end up with x=a(y-b) PLUS a.
You don't have to move it anywhere but factor out an a and divide by whatever was left behind after factoring.
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x=a+b-2ab
isolate the a
x-b=a-2ab
factor an a out of the right side
x-b=a(1-2b)
divide by (1-2b) both sides
(x-b)/(1-2b)=a
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x-a=a(y-b)
distribute
x-a=ay-ab
add a to both sides
x=ay-ab+a
factor out an a on the right
x=a(y-b+1)
divide both sides by (y+b+1)
a=x/(y+b+1)
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The approach to the problem is to usually distribute everything and then take non (in this case) factors of a and move them to the other side.  Then factor an a out of everything that contains it, and divide both sides by what is left over.  In some ways, it is the same kind of problem, solving for a variable.  In other ways, it isn't, because the a is distributed over another pair of variables or constants, and that has to be dealt with.  You could in the second add the a and have x=a(y-b)+a.  That would be factored to x=a(y-b+1), because what was added happened to be a itself.