Question: Solve the inequality for $y$:
$-12 < \frac{8}{3} y$
1. **State the problem:** Solve the inequality $-12 < \frac{8}{3} y$ for $y$.
2. **Recall the rule:** When multiplying or dividing both sides of an inequality by a positive number, the inequality direction stays the same. When multiplying or dividing by a negative number, the inequality direction reverses.
3. **Isolate $y$:** To isolate $y$, divide both sides by $\frac{8}{3}$, which is positive, so the inequality direction remains the same.
4. **Divide both sides:**
$$
-12 < \frac{8}{3} y \\
\Rightarrow \frac{-12}{\frac{8}{3}} < y
$$
5. **Simplify the division:**
$$
\frac{-12}{\frac{8}{3}} = -12 \times \frac{3}{8} = \frac{-36}{8} = \frac{-9}{2}
$$
6. **Final inequality:**
$$
y > \frac{-9}{2}
$$
7. **Interpretation:** The solution is all $y$ values greater than $-\frac{9}{2}$.
**Answer:** $y > -\frac{9}{2}$