1. **State the problem:** Solve the inequality $$22 \geq -7(2 - y) + 2y$$ for $$y$$. 2. **Apply the distributive property:** $$22 \geq -7 \times 2 + (-7) \times (-y) + 2y$$ $$22 \geq -14 + 7y + 2y$$ 3. **Combine like terms on the right side:** $$22 \geq -14 + 9y$$ 4. **Add 14 to both sides to isolate terms with $$y$$:** $$22 + 14 \geq -14 + 14 + 9y$$ $$36 \geq 9y$$ 5. **Divide both sides by 9 to solve for $$y$$:** $$\frac{36}{\cancel{9}} \geq \frac{9y}{\cancel{9}}$$ $$4 \geq y$$ 6. **Rewrite the inequality in a more common form:** $$y \leq 4$$ **Final answer:** $$y \leq 4$$