1. **State the problem:** Solve the equation $5x = x + 12$ for $x$. 2. **Write down the equation:** $$5x = x + 12$$ 3. **Isolate the variable $x$:** Subtract $x$ from both sides to get all $x$ terms on one side: $$5x - x = 12$$ 4. **Simplify the left side:** $$4x = 12$$ 5. **Solve for $x$ by dividing both sides by 4:** $$x = \frac{12}{4}$$ 6. **Simplify the fraction:** $$x = 3$$ **Final answer:** $x = 3$