1. **State the problem:** Solve the equation $$3(x - 5) - 7 = -2(-2x + 4) - 9x$$ for $x$. 2. **Apply the distributive property:** $$3x - 15 - 7 = 4x - 8 - 9x$$ 3. **Simplify both sides:** $$3x - 22 = 4x - 8 - 9x$$ $$3x - 22 = -5x - 8$$ 4. **Add $5x$ to both sides to get all $x$ terms on one side:** $$3x + 5x - 22 = -8$$ $$8x - 22 = -8$$ 5. **Add 22 to both sides to isolate the $x$ term:** $$8x = 14$$ 6. **Divide both sides by 8 to solve for $x$:** $$x = \frac{14}{8} = \frac{7}{4}$$ **Final answer:** $$x = \frac{7}{4}$$