1. **State the problem:** Solve for $x$ in the equation $0.5 + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$. 2. **Rewrite the equation:** $$0.5 + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$$ 3. **Simplify the left side:** $$12960.5 = (50406 - x) \times \frac{5}{8} \times 11.2$$ 4. **Calculate the constant multiplier on the right side:** $$\frac{5}{8} \times 11.2 = \frac{5}{8} \times \frac{112}{10} = \frac{5 \times 112}{8 \times 10} = \frac{560}{80} = 7$$ 5. **Rewrite the equation with the simplified multiplier:** $$12960.5 = (50406 - x) \times 7$$ 6. **Divide both sides by 7 to isolate $(50406 - x)$:** $$\frac{12960.5}{7} = 50406 - x$$ $$1851.5 = 50406 - x$$ 7. **Solve for $x$ by subtracting 1851.5 from 50406:** $$x = 50406 - 1851.5 = 48554.5$$ **Final answer:** $$x = 48554.5$$