1. **State the problem:** Alex has a $\frac{5}{6}$ interest in a partnership. She sold $\frac{5}{8}$ of her interest for 2400. We need to find the total amount of Alex's interest before selling. 2. **Set up the equation:** Let the total amount of Alex's interest before selling be $x$. 3. Alex sold $\frac{5}{8}$ of her interest, so the amount sold is $\frac{5}{8} \times x$. 4. We know this amount equals 2400, so: $$\frac{5}{8}x = 2400$$ 5. To solve for $x$, multiply both sides by the reciprocal of $\frac{5}{8}$, which is $\frac{8}{5}$: $$x = 2400 \times \frac{8}{5}$$ 6. Calculate the right side: $$x = 2400 \times \frac{8}{5} = 2400 \times 1.6 = 3840$$ 7. **Answer:** The total amount of Alex's interest before selling was $3840$.