1. **State the problem:** Solve the equation $2x = 10$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Since $x$ is multiplied by 2, we divide both sides by 2. 3. **Intermediate work:** $$2x = 10$$ Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{10}{2}$$ 4. **Simplify:** $$x = 5$$ 5. **Explanation:** Dividing both sides by 2 cancels the coefficient of $x$, leaving $x$ alone. The right side simplifies to 5, so the solution is $x=5$.