1. **State the problem:** Solve the equation $2x + 8 = 2(x + 4)$. 2. **Write down the formula and rules:** We will use the distributive property and properties of equality to solve for $x$. The distributive property states $a(b + c) = ab + ac$. 3. **Apply the distributive property:** $$2x + 8 = 2 \times x + 2 \times 4$$ $$2x + 8 = 2x + 8$$ 4. **Simplify both sides:** Both sides are equal, so the equation becomes $$2x + 8 = 2x + 8$$ 5. **Subtract $2x$ from both sides:** $$2x + 8 - \cancel{2x} = 2x + 8 - \cancel{2x}$$ $$8 = 8$$ 6. **Interpret the result:** Since the equation simplifies to a true statement $8=8$ with no $x$ left, this means the original equation is true for all values of $x$. **Final answer:** The equation $2x + 8 = 2(x + 4)$ is an identity and holds for all real numbers $x$.