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Yesterday when you phoned me, I was on board the plane/flight. So I can't get through you well, as there was no network coverage.

Yesterday I was about to go over his house, but I had a second thought after I on board the train, so I got off immediately.

I don't like to board my dog anywhere if we go for a journey. We used to take him along with us.

As there was not any day school, I needed to join that far-off/far away boarding school.

Please correct my sentences.
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Yesterday when you phoned me, I was on board the plane/flight, so I couldn't get through to you well, as there was no network coverage.

Yesterday I was about to go over to his house, but I had second thoughts after I got on board the train, so I got off immediately.

I don't like to board my dog anywhere if we go for a journey. We are used to taking him along with us.

As there was not any day school, I needed to join that distant boarding school.
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As there was not any day school, I needed to join that distant boarding school.
Can't I use the phrase "far-off" instead of "distant" because they both somehow mean the same in the dictionary?
I was expanding your vocabulary. 'Far-off' is somewhat poetic for this context. If you insist:

I needed to join that boarding school far away.