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We can use to + infinitive to say why we do something. It tells the other person the reason. We need to have a normal verb as well.
- I went on holiday (this is what I did) to relax (this is why I did it).
- She studies hard to get good marks.
- He gave up cakes to lose weight.
- I'm calling you to ask for your help.
Be careful! In many languages, we use 'for + infinitive'. This is not correct in English.
NOT: I went on holiday for relax.
The main verb can be in any tense. For example:
- Present simple: I exercise every day to stay healthy.
- Present continuous: He's saving money to buy a flat.
- Past simple: I went to university to get a degree.
- Past continuous: She was walking to the shops to buy milk when she met John.
- Future simple: He'll come to the party later to pick up Julia.
- Present perfect: She's gone to the library to study.
We can also use 'in order to + infinitive' and 'so as to + infinitive'. 'In order to' is a bit more formal but the meaning is the same as 'so as to' and 'to + infinitive'.
- I went on holiday to relax.
- I went on holiday in order to relax.
- I went on holiday so as to relax.
We can use a negative infinitive of purpose by adding 'not' before 'to'. Often we do this with 'in order not to' and 'so as not to'.
- I drank coffee in order not to fall asleep.
- He got up very quietly so as not to wake the children.
We can only use the infinitive of purpose if the subject of the main verb and the infinitive of purpose are the same. If they are different, we use 'so that + clause' or 'in order that + clause'.
- I went to the library to study. (I went to the library and I studied - the subject are both 'I'.)
BUT
- I went to the library so that John could study. (I went to the library, but John studied. The two subjects are different - I and John - so we can't use an infinitive of purpose.)
With the verbs 'come' and 'go', we use an infinitive of purpose when they're in a normal tense but we often use 'and + infinitive' with imperatives or after modal verbs.
- I went home to sleep.
- Go home and sleep!
- You must go home and sleep!
Try an exercise about this here.