Let a,b,c be elements of a field F. Prove that if a=/=0, then the equation ax+b=c has a unique solution.
I just learnt fields and polynomials today. This is the only problem that I cannot solve. (I dont even know where to begin)
Solve the equation just as you'd do it in high school (why can you you? Check carefully the given condition), and pay attention to the fact that the solution is given in terms of a,b,c, which makes it unique since a,b,c are unique.