1. **State the problem:** Solve the equation $2x = 64$ 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:** $$2x = 64$$ Divide both sides by 2: $$x = \frac{64}{2}$$ 4. **Simplify:** $$x = 32$$ 5. **Explanation:** Dividing both sides by 2 cancels the multiplication by 2 on the left side, leaving $x$ alone. The right side becomes 64 divided by 2, which is 32. **Final answer:** $x = 32$