1. **State the problem:** Solve the linear equation $7x = 60 + 2x$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse operations. 3. **Step 1:** Subtract $2x$ from both sides to get all $x$ terms on one side: $$7x - 2x = 60 + 2x - 2x$$ which simplifies to $$5x = 60$$ 4. **Step 2:** Divide both sides by 5 to isolate $x$: $$x = \frac{60}{5}$$ 5. **Step 3:** Simplify the fraction: $$x = 12$$ **Final answer:** $x = 12$