Answer
A contradiction.
Work Step by Step
$x+k=x,k\ne0$
We can check the possibilities of this condition by setting x equal to 0 and setting k equal to 1.
$(0)=(1)=1$
The final equation yields a problem. By setting k to any number except 0 and with x held constant, x can never equal its original value before the value of k was added. Therefore, the equation is a contradiction.
$0\ne1$
