1. The problem is to determine whether a given solution is extraneous or not. 2. An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation. 3. To check if a solution is extraneous, substitute it back into the original equation. 4. If the solution satisfies the original equation, it is not extraneous. 5. If it does not satisfy the original equation, it is extraneous. 6. Therefore, the correct phrase is "this solution is not extraneous" if it satisfies the original equation, or "this solution is extraneous" if it does not.