SOLUTION: Solve the following equation for x. ax-b=bx-a

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Question 1071186: Solve the following equation for x.
ax-b=bx-a
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
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Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Solve the following equation for x.
ax-b=bx-a

ax - b = bx - a
ax - bx = b - a
x(a - b) = b - a

Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website!
.
Solve the following equation for x.
ax-b=bx-a
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ax - b = bx - a ---> (ax - bx) + (a-b) = 0 ---> (a-b)x + (a-b) = 0 ---> (a-b)*(x+1) = 0 ---> 1) if a =/= b then x = -1 is the ONLY solution. 2) if a = b, then ANY value of x IS THE SOLUTION.

Answer.   If a=/= b then the only solution is x = -1.

                If a = b then any value of x is the solution.