1. **State the problem:** Solve the inequality $$-\frac{i}{4} \geq 2$$. 2. **Formula and rules:** To solve for $i$, multiply both sides by $-4$ to cancel the denominator. Remember, multiplying or dividing an inequality by a negative number reverses the inequality sign. 3. **Intermediate work:** $$-\frac{i}{4} \geq 2$$ Multiply both sides by $-4$: $$\cancel{-4} \times -\frac{i}{\cancel{4}} \leq 2 \times \cancel{-4}$$ $$i \leq -8$$ 4. **Explanation:** We multiplied both sides by $-4$ to isolate $i$. Because $-4$ is negative, the inequality sign flipped from $\geq$ to $\leq$. 5. **Final answer:** $$i \leq -8$$