1. **State the problem:** Solve the inequality $$-5(x + 7) + 25 \leq 3(2 - x)$$ for $$x$$. 2. **Apply the distributive property:** $$-5x - 35 + 25 \leq 6 - 3x$$ 3. **Combine like terms on the left side:** $$-5x - 10 \leq 6 - 3x$$ 4. **Add $$3x$$ to both sides to get all $$x$$ terms on one side:** $$-5x + 3x - 10 \leq 6 - 3x + 3x$$ 5. **Simplify:** $$-2x - 10 \leq 6$$ 6. **Add 10 to both sides:** $$-2x - 10 + 10 \leq 6 + 10$$ 7. **Simplify:** $$-2x \leq 16$$ 8. **Divide both sides by $$-2$$, remembering to reverse the inequality sign because we divide by a negative number:** $$\cancel{-2}x \geq \frac{16}{\cancel{-2}}$$ 9. **Simplify:** $$x \geq -8$$ **Final answer:** $$x \geq -8$$