1. **Problem statement:** We have a triangle with two sides of lengths 14 and 19. 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 states: $$a + b > c, \quad b + c > a, \quad c + a > b$$ This means the sum of the lengths of any two sides must be greater than the length of the third side. 3. **Apply the triangle inequality:** Let the third side be $x$. Then: $$14 + 19 > x \implies 33 > x \implies x < 33$$ $$14 + x > 19 \implies x > 19 - 14 \implies x > 5$$ $$19 + x > 14 \implies x > 14 - 19 \implies x > -5$$ (which is always true since side lengths are positive) 4. **Combine inequalities:** The third side $x$ must satisfy: $$5 < x < 33$$ 5. **Find smallest whole number:** The smallest whole number greater than 5 is 6. **Final answer:** The smallest possible whole-number length for the third side is **6**.