1. **State the problem:** Solve the inequality $$12[2 - x] \leq 9[3 - 2x]$$. 2. **Distribute the constants:** Multiply inside the brackets: $$12 \times (2 - x) \leq 9 \times (3 - 2x)$$ $$24 - 12x \leq 27 - 18x$$ 3. **Isolate variable terms on one side:** Add $18x$ to both sides to move variable terms to the left: $$24 - 12x + 18x \leq 27 - 18x + 18x$$ $$24 + 6x \leq 27$$ 4. **Isolate the constant term:** Subtract 24 from both sides: $$24 + 6x - 24 \leq 27 - 24$$ $$6x \leq 3$$ 5. **Solve for $x$:** Divide both sides by 6: $$\frac{\cancel{6}x}{\cancel{6}} \leq \frac{3}{6}$$ $$x \leq \frac{1}{2}$$ **Final answer:** $$x \leq \frac{1}{2}$$