i took the time to write down the actiions of the levers. I did not test every possible option by far, so this is not a guarenteed solution, but i mapped what effect the levers had, and steadily progressed to open all the gates.
For what its worth:
lever 1 controls 3 and 6 simultaniously both open and close
lever 2 controls 5 only close
lever 3 opens 6, close 2
lever 4 controls 2 can only open
lever 5 controls 1 can only close
lever 6 controls 5 can only open
lever 7 opens 1, closes 2 and 6
By following these, and simply opening the gates that are closed with the appropriate lever, you should be able to open them all. Hope it works for you guys as well!