Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 4/5n−12>24 , where n equals the number, to help solve this problem. Solve her inequality.

To solve the inequality \( \frac{4}{5}n - 12 > 24 \), we can follow these steps:

1. Add 12 to both sides:

   \[ \frac{4}{5}n - 12 + 12 > 24 + 12 \]

   This simplifies to:

   \[ \frac{4}{5}n > 36 \]

2. Multiply both sides by \( \frac{5}{4} \) to isolate \( n \):

   \[ n > 36 \times \frac{5}{4} \]

   Calculating \( 36 \times \frac{5}{4} \):

   \[ 36 \times \frac{5}{4} = 36 \times 1.25 = 45 \]

   So we have:

   \[ n > 45 \]

Thus, the solution to the inequality is

\[ \boxed{(45, \infty)} \]

This means all values of \( n \) that are greater than 45 satisfy the original inequality.