1. The problem is to solve the equation $1 = 1$. 2. This equation states that the number 1 is equal to the number 1. 3. Since both sides of the equation are identical, the equation is true for all values (it is an identity). 4. Therefore, the solution is that the equation holds true universally, and there is no variable to solve for. Final answer: The equation $1 = 1$ is always true.