1. The problem is to solve the equation $x + 1 = 2x + 2$ for $x$. 2. We use the principle of equality: whatever operation is done on one side must be done on the other side to keep the equation balanced. 3. Start by subtracting $x$ from both sides: $$x + 1 - x = 2x + 2 - x$$ which simplifies to $$1 = x + 2$$ 4. Next, subtract 2 from both sides: $$1 - 2 = x + 2 - 2$$ which simplifies to $$-1 = x$$ 5. Therefore, the solution is: $$x = -1$$ 6. This matches the answer given, so the solution is correct.