The symbol that produces an inequality with a finite number of nonsolutions is \( \leq \) (less than or equal to) or \( \geq \) (greater than or equal to).
When using these symbols, we can create an inequality that bounds values, leading to a limited set of solutions.
However, specifically, the answer is:
≤ or ≥ (both can define a finite set of nonsolutions depending on the context).
If the question is looking for only one, then you can choose ≤ as it typically suggests a range that includes a specific upper limit.