What strategy is most appropriate when one has a solution that may meet the needs of others who can accept or reject it?

The most appropriate strategy in a situation where you have a solution that may meet the needs of others who can accept or reject it is convincing. This approach involves persuading others to see the value in your solution and encouraging them to embrace it.

When you are convincing, you engage with the audience by presenting your solution in a way that highlights its benefits, reaffirms its relevance to their needs, and addresses potential concerns. This strategy effectively fosters acceptance and is crucial when the outcome depends on the willingness of others to adopt the proposed solution. Convincing requires clear communication, confidence in your proposal, and an understanding of the audience’s perspective, making it a dynamic and interactive process.

The other strategies listed, while potentially useful in various contexts, do not focus specifically on the act of persuading others to accept a proposal. Supporting would imply backing someone else's idea, providing a compelling rationale could enhance an argument but doesn't actively engage in persuasion, and listening, while vital for understanding others' perspectives, does not directly advocate for one's solution.