1. **State the problem:** Solve the equation $$5 + 6(x + 9) = 59 - 9(3x + 1)$$ and check the solution. 2. **Expand both sides:** $$5 + 6x + 54 = 59 - 27x - 9$$ 3. **Combine like terms:** $$5 + 54 = 59 - 9$$ $$59 + 6x = 50 - 27x$$ 4. **Bring variables to one side and constants to the other:** $$6x + 27x = 50 - 59$$ $$33x = -9$$ 5. **Solve for $x$ by dividing both sides by 33:** $$x = \frac{-9}{33}$$ $$x = \frac{\cancel{ -9 }}{\cancel{33}} = -\frac{3}{11}$$ 6. **Check the solution by substituting $x = -\frac{3}{11}$ back into the original equation:** Left side: $$5 + 6\left(-\frac{3}{11} + 9\right) = 5 + 6\left(\frac{96}{11}\right) = 5 + \frac{576}{11} = \frac{55}{11} + \frac{576}{11} = \frac{631}{11}$$ Right side: $$59 - 9\left(3\times -\frac{3}{11} + 1\right) = 59 - 9\left(-\frac{9}{11} + 1\right) = 59 - 9\left(\frac{2}{11}\right) = 59 - \frac{18}{11} = \frac{649}{11} - \frac{18}{11} = \frac{631}{11}$$ Both sides equal $$\frac{631}{11}$$, so the solution is correct. **Final answer:** $$x = -\frac{3}{11}$$