Two sides of a triangle have lengths 9 and 15. What is the smallest possible integer length for the third side?

The triangle inequality says the third side $x$ must be longer than the difference of the other two sides and shorter than their sum: $15 - 9 < x < 15 + 9$, so $6 < x < 24$. The smallest integer strictly greater than 6 is 7. A side of 6 would make $9 + 6 = 15$, which only flattens the triangle into a straight line, so it is not allowed. A common wrong answer is 6, from allowing equality, and another is 1, which ignores the inequality entirely. Both bounds are strict.