1. **State the problem:** We want to find an equation that shows buying one item at regular price $x$ and a second identical item at 50% off is the same as buying both items for 25% off. 2. **Understand the terms:** - Regular price of one item: $x$ - Second item at 50% off: $0.5x$ - Total price when buying separately: $x + 0.5x$ - Buying both items for 25% off means paying 75% of the total regular price for two items: $2 \times 0.75x$ 3. **Write the equation for the relationship:** $$x + 0.5x = 2 \times 0.75x$$ 4. **Simplify the left side:** $$x + 0.5x = 1.5x$$ 5. **Simplify the right side:** $$2 \times 0.75x = 1.5x$$ 6. **Check equality:** $$1.5x = 1.5x$$ This confirms the correct equation is $x + 0.5x = 2(0.75x)$. **Final answer:** Option D.