Answer:
- I went to the supermarket yesterday to buy some groceries.
- The gentleman was kind enough to carry the suitcase for me.
- That popular restaurant might be fully booked tonight.
- The woman was glad to see her family after she woke from the coma.
- We had better see the doctor about that rash.
Step-by-step explanation:
Infinitives without to are called bare infinitives, and they are usually used after modal verbs -like might- and certain expressions like had better and would rather.
Infinitives with to are referred to as full infinitives, and they can indicate purpose as well as be employed after certain verbs, adjectives and phrases with too and enough.