Final answer:
The social worker should first assess the extent to which the client's life is affected by excessive internet use, as it represents a comprehensive approach to understand and address the issue.
Step-by-step explanation:
When a social worker meets a client concerned about excessive internet use that is impacting interpersonal relationships, the first step would be to determine the degree to which the client's life is affected. This holistic assessment includes understanding the breadth and depth of the potential problem, including the number of hours spent online, the nature of online activities, and the resulting consequences on offline relationships and daily functioning. This critical evaluation will help in formulating an effective intervention strategy that addresses the core issues and promotes healthier online behaviors and improved interpersonal relationships.