Before you do this, cut up the credit cards, or you'll wind up back in the same spot only WITHOUT the safety net of the home equity loan.
You didn't say what you planned to do with the other $3000 ($10,000 HEL - $7000 credit card debt = $3000). I hope you aren't going to use this $3000 as an emergency fund. It would be better to take just the amount you need to pay off the credit cards (after you have cut them up) and then start making 'payments' to a savings account for emergencies because you won't get 7.5% return on a savings account.
An even better solution (if you mortgage rate isn't much lower than the 7.5%) would be to refinance and take out cash. This way, you have only ONE mortgage payment (instead of two) and will have money available to set aside for the emergency fund so you won't have to use the credit cards WHEN emergencies happen (and you KNOW they will).
Either way, the interest SHOULD be tax-deductible (as opposed to the interest on the credit cards, which is not).
The key here is to stop spending money you don't have by using credit cards. EVERYTHING you buy on a credit card costs more than paying cash when you include the interest and fees. Put money in a savings account for emergencies and money in ANOTHER account for that new computer, or big screen TV or newer (NEVER new) car.
http://www.daveramsey.com or check out one of his books (from the library) - "Financial Peace" or "Your Total Money Makeover"