1. **State the problem:** Solve the equation $$3(-9 - 4x) = -5(2x - 1)$$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3 \times (-9) + 3 \times (-4x) = -5 \times 2x + (-5) \times (-1)$$ which simplifies to $$-27 - 12x = -10x + 5$$ 3. **Rearrange the equation:** Move all terms involving $x$ to one side and constants to the other. Add $12x$ to both sides: $$-27 - \cancel{12x} + 12x = -10x + 12x + 5$$ which simplifies to $$-27 = 2x + 5$$ 4. **Isolate $x$:** Subtract 5 from both sides: $$-27 - 5 = 2x + \cancel{5} - 5$$ which simplifies to $$-32 = 2x$$ 5. **Solve for $x$:** Divide both sides by 2: $$\frac{-32}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to $$x = -16$$ **Final answer:** $$x = -16$$