1. **State the problem:** Solve the equation $$9(x + 4) - 4[x - 6(5 + x)] = \frac{5}{3}(x - 8)$$. 2. **Use the distributive property:** $$9x + 36 - 4[x - 30 - 6x] = \frac{5}{3}x - \frac{40}{3}$$ 3. **Simplify inside the brackets:** $$9x + 36 - 4[x - 30 - 6x] = 9x + 36 - 4[x - 30 - 6x]$$ Inside the bracket: $$x - 30 - 6x = -5x - 30$$ 4. **Distribute -4:** $$9x + 36 - 4(-5x - 30) = \frac{5}{3}x - \frac{40}{3}$$ $$9x + 36 + 20x + 120 = \frac{5}{3}x - \frac{40}{3}$$ 5. **Combine like terms on the left:** $$29x + 156 = \frac{5}{3}x - \frac{40}{3}$$ 6. **Multiply entire equation by 3 to clear denominators:** $$3(29x + 156) = 3\left(\frac{5}{3}x - \frac{40}{3}\right)$$ $$87x + 468 = 5x - 40$$ 7. **Bring all terms involving $x$ to one side and constants to the other:** $$87x - 5x = -40 - 468$$ $$82x = -508$$ 8. **Solve for $x$:** $$x = \frac{-508}{82} = -\frac{254}{41}$$ **Final answer:** $$x = -\frac{254}{41}$$