10. \( -8<\frac{2}{3} n \)

To solve the inequality \( -8 < \frac{2}{3} n \), start by isolating \( n \). Multiply both sides by \( \frac{3}{2} \) (which is positive, so it won't change the inequality direction). This gives you \( -8 \cdot \frac{3}{2} < n \), simplifying to \( -12 < n \) or \( n > -12 \). So the solution set is all values greater than \(-12\). Now, if you wanted to check your solution, you can substitute a number greater than -12, like -11. Plugging it back into the original inequality gives \( -8 < \frac{2}{3} \cdot (-11)\), which simplifies to \( -8 < -\frac{22}{3}\) or roughly -7.33. Since that is true, your solution holds!