How to delete apps on IPhone?

I want to delete non preinstalled apps from my iPhone 4S. I know to hold down the app until it "wiggles" but no X is in the corner. When I first got the phone I could delete apps but after a couple updates the X disappeared! How do I remove the apps without the X?

I've always done it with the X as you said but I believe you can also go into the view of all apps in your settings and uninstall from there also.

Without the X, wow that's a problem! But what you can do is go to settings, than click general, once you get in click usage. All your apps appear in a list. Click on the app you want to delete on the list and under the icon of the app and how much space on your memory it takes up it say delete app and then a tab at the bottom appears and all you do is confirm the removal! Hope I could help!