1. **State the problem:** Solve the equation $x = 12 + \frac{2x}{2}$ for $x$. 2. **Rewrite the equation:** The equation is $x = 12 + \frac{2x}{2}$. 3. **Simplify the fraction:** $\frac{2x}{2} = x$, so the equation becomes: $$x = 12 + x$$ 4. **Subtract $x$ from both sides:** $$x - \cancel{x} = 12 + x - \cancel{x}$$ $$0 = 12$$ 5. **Interpret the result:** The statement $0 = 12$ is false, which means there is no solution to the equation. **Final answer:** There is no solution to the equation $x = 12 + \frac{2x}{2}$ because it leads to a contradiction.