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To further clarify, carrying a balance means (at least to me) not paying your entire balance each billing cycle. That is, you can still let a balance report and pay it in full when you get the regular bill. You won't incur any interest rate charges.
If, however, you are trying to limit the number of cards that report balances in order to boost your score, then you should follow the sage advice proffered by the mods. Since you're using your cards, they won't be closed for inactivity.
To payoff or not (before or after the closing date) doesnt matter I guess. As long as you keep the balance low like 5% of your credit limit when the statement closes.