1. **State the problem:** Solve the equation $0.5x + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$ for $x$. 2. **Write the equation clearly:** $$0.5x + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$$ 3. **Simplify the right side:** Calculate $\frac{5}{8} \times 11.2$: $$\frac{5}{8} \times 11.2 = \frac{5 \times 11.2}{8} = \frac{56}{8} = 7$$ So the equation becomes: $$0.5x + 12960 = 7(50406 - x)$$ 4. **Distribute 7 on the right side:** $$0.5x + 12960 = 7 \times 50406 - 7x$$ Calculate $7 \times 50406$: $$7 \times 50406 = 352842$$ So: $$0.5x + 12960 = 352842 - 7x$$ 5. **Bring all $x$ terms to one side and constants to the other:** Add $7x$ to both sides: $$0.5x + 7x + 12960 = 352842$$ Combine like terms: $$7.5x + 12960 = 352842$$ Subtract 12960 from both sides: $$7.5x = 352842 - 12960 = 339882$$ 6. **Solve for $x$:** $$x = \frac{339882}{7.5}$$ Calculate: $$x = 45317.6$$ **Final answer:** $$x = 45317.6$$