1. **State the problem:** Solve the inequality $4x + 4y \le 24$ for $y$ in terms of $x$. 2. **Rewrite the inequality:** We want to isolate $y$ on one side. $$4x + 4y \le 24$$ 3. **Subtract $4x$ from both sides:** $$\cancel{4x} + 4y - \cancel{4x} \le 24 - 4x$$ which simplifies to $$4y \le 24 - 4x$$ 4. **Divide both sides by 4:** $$\frac{4y}{\cancel{4}} \le \frac{24 - 4x}{\cancel{4}}$$ which simplifies to $$y \le 6 - x$$ 5. **Interpretation:** The inequality $y \le 6 - x$ represents all points $(x,y)$ on or below the line $y = 6 - x$. **Final answer:** $$y \le 6 - x$$