1. **State the problem:** Solve the equation $$2 = \frac{100}{x}$$ for $x$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides of the equation by $x$ to eliminate the fraction. 3. **Multiply both sides by $x$:** $$2 \times x = \frac{100}{\cancel{x}} \times x$$ This simplifies to: $$2x = 100$$ 4. **Isolate $x$ by dividing both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{100}{2}$$ $$x = 50$$ 5. **Final answer:** $$x = 50$$ This means that when $x$ is 50, the equation $2 = \frac{100}{x}$ holds true.