1. **Problem statement:** We have a triangle with two sides of lengths 6 and 1. We want to find the smallest possible whole-number length for the third side. 2. **Formula and rule:** The triangle inequality states that the sum of the lengths of any two sides must be greater than the length of the third side. For sides $a$, $b$, and $c$, this means: $$ a + b > c, \quad a + c > b, \quad b + c > a $$ 3. **Apply the triangle inequality:** Let the third side be $x$. Then: - $6 + 1 > x \implies 7 > x$ - $6 + x > 1 \implies x > -5$ (always true since $x$ is positive) - $1 + x > 6 \implies x > 5$ 4. **Combine inequalities:** From above, $x$ must satisfy: $$ 5 < x < 7 $$ 5. **Find smallest whole number:** The smallest whole number greater than 5 and less than 7 is 6. **Final answer:** The smallest possible whole-number length for the third side is **6**.