1. This lesson features many uses of the word 答应. However, notice how the word can vary in meaning from “commit” to “agree” to “promise”, as seen in the following examples:
a. 我不得不答应.
b. 最后他总算答应了.
c. 答应别人了以后就不再改变.

2. can also mean “invite”, as seen in 比如说今天晚上你只想待在家里不想去任何地方. 但是你的同事突然找你一起去一个派对可是你想不到理由来拒绝他你就可以这么说.

3. 经过 has a more abstract meaning of “encountering”, as seen in 不过经过你的努力并且试着让对方了解答应这件事情的好处最后他总算答应了.