Apps will not open on iPhone 4s

I have a iPhone 4s and it's my first iPhone. I'm having problems with apps (Facebook, Instagram, games, etc). When I first installed them they worked fine, but after a while they all stopped working - when I touch one of the apps to open it, it will shake, my screen will briefly go black (like it's opening it), and then I'll be back to my main screen again. I uninstalled and reinstalled all of the apps, which worked for a bit, but now I'm back to the same problem.

Any advice/suggestions would be great, thank you 🙂