Acts and Paul

It is said that Paul went to preach to the gentiles. His last words were: Acts 28,28 "Let it be known to you that this salvation of God has been sent to the Gentiles; they will listen." this is only one example among many.
However, through all the book of Acts he is preaching in synagogues always to the Jews and always there are gentiles around.
In Pauls authentic letters it is never mentioned he is preaching in synagogues, Pauls letters clearly show us that the mission among the Jews in Israel failed.
The autor of Acts wants us to believe many Jews accepting jesus as their messaiah.

Acts 1,8 "But you will receive power when the holy Spirit comes upon you, and you will be my witnesses in Jerusalem, throughout Judea and Samaria, and to the ends of the earth."
Jesus talk to the apostels telling them to be his witnesses in Israel, not in other places.
Jesus didn't mention preaching to the gentiles.