1. **State the problem:** Solve the equation $2x + 1 = x + 5$ for $x$. 2. **Write down the equation:** $$2x + 1 = x + 5$$ 3. **Isolate the variable terms on one side:** Subtract $x$ from both sides: $$2x + 1 - \cancel{x} = \cancel{x} + 5 - x$$ which simplifies to $$x + 1 = 5$$ 4. **Isolate $x$ by subtracting 1 from both sides:** $$x + 1 - \cancel{1} = 5 - \cancel{1}$$ which simplifies to $$x = 4$$ 5. **Final answer:** $$\boxed{4}$$