1. **State the problem:** Solve the equation $$4x + (5x - (6x - (7x - (8x - 9)))) = 10$$ for $x$. 2. **Understand the problem:** This is a nested expression with multiple parentheses. We will simplify from the innermost parentheses outward. 3. **Simplify the innermost parentheses:** $$8x - 9$$ 4. **Next level:** $$7x - (8x - 9) = 7x - 8x + 9 = -x + 9$$ 5. **Next level:** $$6x - (7x - (8x - 9)) = 6x - (-x + 9) = 6x + x - 9 = 7x - 9$$ 6. **Next level:** $$5x - (6x - (7x - (8x - 9))) = 5x - (7x - 9) = 5x - 7x + 9 = -2x + 9$$ 7. **Substitute back into the original equation:** $$4x + (-2x + 9) = 10$$ 8. **Simplify:** $$4x - 2x + 9 = 10$$ $$2x + 9 = 10$$ 9. **Solve for $x$:** $$2x = 10 - 9$$ $$2x = 1$$ $$x = \frac{1}{2}$$ **Final answer:** $$x = \frac{1}{2}$$