He following sentences using ‘careful,’ ‘live,’ and ‘life’ are correct and acceptable, aren’t they?

The following sentences using ‘careful,’ ‘live,’ and ‘life’ are correct and acceptable, aren’t they? If not, what correction do I have to make?

1. Without careful attention to your diet, you cannot continue to live a productive life.

2. Without paying careful attention to your diet, you cannot continue living a productive life.

3. Without paying careful attention to your diet, you cannot continue to live productively.