verb
1
BAD : Her parents have offered me to go on holiday with them.
GOOD : Her parents have invited me to go on holiday with them.
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offer to do sth = express willingness to do something: 'She's offered to help me.'
invite sb to (do) sth = ask someone if they would like to come to a party, wedding, etc, or join you in a social activity: 'Have you invited Mark and Valerie to the party?'
2
BAD : The old man then offered something to eat to the little boy.
GOOD : The old man then offered the little boy something to eat.
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The usual pattern is offer sb sth ( offer + indirect object + direct object): 'He offered me a job.' 'They've offered Maria a place on the intermediate course.'
Use offer something to someone only when the direct object is a pronoun or is much shorter than the indirect object: 'She offered it to George but he didn't want it.' 'I offered the apple to the first child that could answer my question.'