1. **State the problem:** Solve the equation $$\frac{1}{2}(x+18) = 4(2x-6) - 9x$$. 2. **Distribute and simplify both sides:** $$\frac{1}{2}x + \frac{1}{2} \times 18 = 4 \times 2x - 4 \times 6 - 9x$$ $$\frac{1}{2}x + 9 = 8x - 24 - 9x$$ 3. **Combine like terms on the right side:** $$\frac{1}{2}x + 9 = (8x - 9x) - 24$$ $$\frac{1}{2}x + 9 = -x - 24$$ 4. **Add $x$ to both sides to get all $x$ terms on one side:** $$\frac{1}{2}x + x + 9 = -24$$ $$\frac{3}{2}x + 9 = -24$$ 5. **Subtract 9 from both sides:** $$\frac{3}{2}x = -24 - 9$$ $$\frac{3}{2}x = -33$$ 6. **Multiply both sides by the reciprocal of $\frac{3}{2}$, which is $\frac{2}{3}$, to solve for $x$:** $$x = -33 \times \frac{2}{3}$$ $$x = -22$$ **Final answer:** $$x = -22$$