1. **State the problem:** Solve the proportion $$\frac{11}{5} = \frac{10}{x}$$ for $x$ and round the answer to the nearest tenth. 2. **Use the cross-multiplication formula:** For proportions $$\frac{a}{b} = \frac{c}{d}$$, cross-multiply to get $$a \times d = b \times c$$. 3. **Apply cross-multiplication:** $$11 \times x = 5 \times 10$$ 4. **Simplify the right side:** $$11x = 50$$ 5. **Solve for $x$ by dividing both sides by 11:** $$x = \frac{50}{11}$$ 6. **Show cancellation:** $$x = \frac{\cancel{50}}{\cancel{11}}$$ (no common factors to cancel, so fraction remains as is) 7. **Calculate the decimal value:** $$x \approx 4.5454...$$ 8. **Round to the nearest tenth:** $$x \approx 4.5$$ **Final answer:** $$\boxed{4.5}$$