1. **State the problem:** Solve for $x$ in the equation $x + 1 = 2x + 2$. 2. **Write the equation:** $$x + 1 = 2x + 2$$ 3. **Isolate the variable $x$ on one side:** Subtract $x$ from both sides: $$\cancel{x} + 1 = 2x + 2 - \cancel{x}$$ which simplifies to $$1 = x + 2$$ 4. **Isolate $x$ completely:** Subtract 2 from both sides: $$1 - 2 = x + 2 - 2$$ which simplifies to $$-1 = x$$ 5. **Final answer:** $$x = -1$$ This means the value of $x$ that satisfies the equation is $-1$.