1. The problem statement, all variables and given/known data Prove that if a,b,c are elements of a field. than a+b = a+c implies b=c 2. Relevant equations a + (-a) = 0 0 + a = a 3. The attempt at a solution The solution i found is: a+b = a+c a+b+(-a) = a+c+(-a) 0+b = 0+c b=c what i'm not sure about is that since i don't know that a+b = a+c is the same as b=c, in other words, that i can subtract from both sides of an equation. can i assume that i can add to both sides of the equation?