If the broken tip cannot be found after searching, what should be done next?

When dealing with a situation where a broken tip from an instrument cannot be located after a thorough search, it's crucial to take action that prioritizes patient safety. Recommending a chest x-ray to check for aspiration is the appropriate course of action because there is a potential risk that the broken piece may have been inhaled into the respiratory tract. A chest x-ray can confirm whether or not the tip is present in the lungs, which is vital for ensuring the patient's safety and addressing any complications that may arise from aspiration.

Taking this step ensures that any health risks associated with the aspirated object are managed promptly, reducing the likelihood of respiratory distress or other complications. This proactive approach is essential in dental hygiene practice, where the safety and well-being of the patient are always the top priorities.

Other options, while possibly relevant in broader contexts, do not directly address the immediate concern of potential aspiration or its consequences. Monitoring symptoms or scheduling a follow-up appointment does not adequately address the urgency of ruling out aspiration, and ignoring the issue could lead to severe complications for the patient. Thus, the recommendation for a chest x-ray is the most responsible and effective choice in this scenario.