have an iphone 4s. have attempted to delete apps but when touch screen and hold it for few seconds apps jiggle but no x shown. What happened and how can delete apps at this point

I have an iphone 4s. I have attempted to delete apps but when I touch the screen and hold it for a few seconds, the apps jiggle but there is no "x" shown. What happened and how can I delete apps at this point.

I am trying to update the apps in my phone but it says I dont have enough local storage to download and to manage it in settings. I went into it and attempted to It says I have 25gb storage and 16.7gb available. How else can I make enough room on my phone to get my apps to update. When I go into manage storage and then into "my phone" it says I have filled 8.2gb. Trying to make more room. Help please.