Seeing the Galilean Moons with Celestron 7x50 Binoculars

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I have a pair of Celestron 7x50 binoculars. I was looking at Jupiter a few nights ago. Sometimes, I imagined I could just barely make out a row of specks that might have been the Galilean moons, but it was really hard to hold the binoculars steady enough to be certain. Is it at least theorectically possible to see the moons at this magnification? I mean, Galileo himself couldn't have had much better available to him, right?
 
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Yes, it is possible to see them with a decent pair of binoculars.
 
You should be able to see them relatively easily with virtually any binoculars unless you have light polluted skies. Theoretically, they should be visible naked-eye, as none are dimmer than magnitude 6. Try getting something to lean the binoculars against to stabilize them.