x = x + 2
For this kind of equation, the general rule applies which is, collect like terms. That is, bring the unknown variables to one side of the equation and bring the known (or constants) to the other side.
We move the x on the right to the left and we now have this;
x - x = 2
**Note that when a positive value crosses from one side of the equation to the other, it becomes negative (and vice versa). Hence x has now become a negative as soon as it crossed to the left.**
x - x = 2
0 = 2
Now we know that this is not possible, that is 0 does not equal to 2.
At this point its safe to say that the equation has NO SOLUTION.
This is because upon close observation, the equation ideally should read;
x = x
However, the moment the constant 2 comes into the equation, then the value of x on the left must change by a factor of "+ 2"
In conclusion, there is no value of x that can satisfy this equation. Because if you attempt to input "x = 0 on one side of the equation, you MUST do the same on the other side of the equation.