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You can be approved for the Next Express credit card with your credit score but you will need to work hard to rebuild your credit and not to make it worse because this credit card cones with high 24.99% APR. If you carry a balance on this card, the interest will accrue fast. If you are the one who pays the card balances in full and on time, this card can help you rebuild credit. If not, consider getting a regular credit card with a lower interest rate.
By the way, you can also apply for a secured credit card. Don't worry about a security deposit. It's not as bad as you'd think, and it is usually refundable. For example, if you apply for the Discover it® Secured Credit Card, you won't pay annual fee. Also, you will earn 2% cash back at Gas Stations and Restaurants on up to $1,000 in combined purchases each quarter and 1% cash back on all other purchases. By the way, Discover matches all cash back you've earned after first year (if you are a new cardmember). So, you can earn more than you spent on security deposit during the first year.