You cannot use the security deposit to cover back rent unless your lease agreement allows you to do so. I would serve an updated 3-day notice and then proceed with an eviction.
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As previously stated, your best option is probably to proceed with the eviction. However, you will want to be absolutely certain that the three-day notice you provided the tenant is correct. If you file the eviction based upon a defective notice, you run the chance of having the case dismissed.
With regard to providing the tenant notice of your entry, you should look to your lease. A properly constructed lease should provide for specifics regarding how to provide notice, the means of delivery, and timing. Keep in mind that if the tenant does not vacate at the end of their lease, you will still have to resort to eviction to get them out.
This communication is not intended to, and does not, create an attorney/client relationship. You are encouraged to consult with an attorney in your area to discuss your case in person. Roberto M. Vazquez, Esq. and the Morey Law Firm, P.A. practice law throughout the state of Florida. Please visit our website at www.moreylawfirm.com.Ask a similar question