To check if \( k = 7 \) is a solution to the inequality \( 31 > \frac{77}{k} \), we first substitute \( k = 7 \) into the inequality:
\[ 31 > \frac{77}{7} \]
Now, calculate \( \frac{77}{7} \):
\[ \frac{77}{7} = 11 \]
Now, the inequality becomes:
\[ 31 > 11 \]
This statement is true. Therefore, \( k = 7 \) is indeed a solution to the inequality.