To solve the equation \( x - 7 = 24 \), you need to isolate \( x \).
Start by adding 7 to both sides of the equation:
\[ x - 7 + 7 = 24 + 7 \]
This simplifies to:
\[ x = 31 \]
Therefore, the integer that makes the subtraction sentence true is \( \boxed{31} \).