My organic eggs have a date of June 24 on them; today is June 28. Can I still cook them? (I am not used to purchasing organic eggs.)
Check again, the date should be 'sell by' rather than 'eat by'. If you're in the US, you should have at least a couple weeks to eat them after the sell by date.
use a glass of water, if they float to the top not good, if the sink they are fresh, if they kinda float but not to the top they are ok