1. Stating the problem: Solve the first equation $12x = 120$ for $x$. 2. Formula and rules: To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 12. 3. Intermediate work: $$12x = 120$$ Divide both sides by 12: $$\frac{\cancel{12}x}{\cancel{12}} = \frac{120}{12}$$ 4. Simplify the right side: $$x = 10$$ 5. Explanation: We isolated $x$ by dividing both sides by 12, which cancels the 12 on the left side, leaving $x$ alone. Dividing 120 by 12 gives 10, so the solution is $x=10$. Final answer: $x = 10$