What is the answer to Ax - c = b

Depends on what you are talking about, what is A, x, c and b.

If A is an invertible matrix and x, c, b are vectors of correct dimensions you get

Ax=b+c

x=A^ (-1) (b+c)

if x is a variable and A, c, b are constants you get

Ax=b+c

x = (b+c) / A

X = (b + c) / A is the correct answer