1. **State the problem:** Solve the inequality $$-4 + 4(4r - 8) \leq 10r - 9 - 6$$ for $r$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses. $$-4 + 4 \times 4r - 4 \times 8 \leq 10r - 9 - 6$$ $$-4 + 16r - 32 \leq 10r - 15$$ 3. **Combine like terms on the left side:** $$(-4 - 32) + 16r \leq 10r - 15$$ $$-36 + 16r \leq 10r - 15$$ 4. **Isolate variable terms on one side and constants on the other:** Subtract $10r$ from both sides. $$-36 + 16r - 10r \leq 10r - 10r - 15$$ $$-36 + \cancel{16r - 10r} \leq \cancel{10r - 10r} - 15$$ $$-36 + 6r \leq -15$$ 5. **Add 36 to both sides to isolate the term with $r$:** $$-36 + 6r + 36 \leq -15 + 36$$ $$\cancel{-36 + 36} + 6r \leq 21$$ $$6r \leq 21$$ 6. **Divide both sides by 6 to solve for $r$:** $$\frac{6r}{\cancel{6}} \leq \frac{21}{\cancel{6}}$$ $$r \leq \frac{21}{6}$$ 7. **Simplify the fraction:** $$r \leq \frac{7}{2}$$ **Final answer:** $$r \leq \frac{7}{2}$$