1. **State the problem:** Solve the inequality $$12[2 - 9c] \leq 9[3 - 2d]$$ for variables $c$ and $d$. 2. **Distribute the constants inside the brackets:** $$12 \times 2 - 12 \times 9c \leq 9 \times 3 - 9 \times 2d$$ which simplifies to $$24 - 108c \leq 27 - 18d$$ 3. **Rearrange terms to isolate variables on one side and constants on the other:** Subtract 24 from both sides: $$24 - 108c - 24 \leq 27 - 18d - 24$$ which simplifies to $$-108c \leq 3 - 18d$$ 4. **Rewrite the inequality:** $$-108c \leq 3 - 18d$$ 5. **Divide both sides by -108 to solve for $c$, remembering to reverse the inequality sign because dividing by a negative number reverses inequality:** $$c \geq \frac{3 - 18d}{-108}$$ 6. **Simplify the fraction:** $$c \geq \frac{3}{-108} - \frac{18d}{-108} = -\frac{1}{36} + \frac{1}{6}d$$ 7. **Final solution:** $$c \geq \frac{1}{6}d - \frac{1}{36}$$ This means $c$ must be greater than or equal to $\frac{1}{6}d - \frac{1}{36}$ for the inequality to hold.