Question: Solve the inequality for $u$.
$$\frac{12}{11} \geq -16u$$
Simplify your answer as much as possible.
1. **State the problem:** Solve the inequality $$\frac{12}{11} \geq -16u$$ for $u$.
2. **Recall the rule:** When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.
3. **Isolate $u$:** Divide both sides by $-16$. Since $-16$ is negative, reverse the inequality sign:
$$\frac{12}{11} \geq -16u \implies \frac{12}{11} \div (-16) \leq u$$
4. **Simplify the division:**
$$\frac{12}{11} \div (-16) = \frac{12}{11} \times \frac{1}{-16} = \frac{12}{11} \times \frac{-1}{16} = -\frac{12}{176}$$
5. **Simplify the fraction:**
$$-\frac{12}{176} = -\frac{3}{44}$$
6. **Final solution:**
$$u \geq -\frac{3}{44}$$
**Answer:** $$u \leq -\frac{3}{44}$$ because the inequality sign reversed when dividing by negative.
Note: Step 3 shows the reversal of the inequality sign due to division by a negative number.