1. **Problem statement:** We have a triangle with two sides of lengths 15 and 7. We want to find the smallest possible whole-number length for the third side. 2. **Formula and rule:** For any triangle with sides $a$, $b$, and $c$, the triangle inequality must hold: $$ |a - b| < c < a + b $$ This means the length of any side must be greater than the difference of the other two sides and less than their sum. 3. **Apply the triangle inequality:** Given sides 15 and 7, let the third side be $x$. - Lower bound: $$x > |15 - 7| = 8$$ - Upper bound: $$x < 15 + 7 = 22$$ 4. **Find the smallest whole number:** Since $x$ must be greater than 8, the smallest whole number satisfying this is 9. **Final answer:** The smallest possible whole-number length for the third side is **9**.