Final answer:
The equation x - 2 = - (-x) simplifies to -2 = 0 after negating the negative sign on the right-hand side and subtracting x from both sides. This is not possible for any value of x because -2 cannot equal 0, indicating a mistake in the question premise.
Step-by-step explanation:
The equation you're given is x - 2 = - (-x). To complete and solve this equation for all values of x, we simply need to simplify it. First, we negate the negative sign on the right-hand side of the equation, which will change - (-x) to x. The equation now reads x - 2 = x. Then, to solve for x, we need to get x alone on one side of the equation, so we subtract x from both sides, as you always want to do the same operation to both sides of the equation. The resulting equation is -2 = 0, because x - x cancels out. Clearly, this is not true for any value of x because -2 can never equal 0. It seems there might be a mistake in the premise of the problem since the equation given cannot be true for all values of x.