For the system x > k and x < 10 to have at least one solution, k must be less than what value?

The system $x > k$ and $x < 10$ asks for numbers that are greater than $k$ and less than 10 at the same time. Such numbers exist only if there is room between $k$ and 10, which means $k < 10$. If $k = 10$, the conditions become $x > 10$ and $x < 10$, which no number satisfies. If $k > 10$, the situation is even worse. So $k$ must be less than 10. A common wrong answer is 9, which assumes an integer solution is required, but the problem does not say so; for $k = 9.5$, the value $x = 9.7$ works. The strict inequalities mean $k = 10$ itself fails, but any $k$ below 10 works.