Q: I can't delete old pictures from my iphone (older than a year)

My sister has an iPhone 4S and can't update to the new OS because she is out of memory.  Turns out she was syncing her photos from her computer to her phone (we got that straightened out), but now she can't delete the photos in her phone if they are over about 1 year old.  It doesn't matter if they are pictures that she took with her phone, or if they were imported from her PC, the garbage can icon is either grayed out or not there.  So I checked my iPhone 6, and even though I have the updated IOS and 64 GB of storage, I can't delete old pictures either.   In Photos (not albums), I am selecting a photo taken with my phone from April 2010 - the garbage can is grayed out and my only options are to upload the photo to the regular places or "add to" a new file that I can to create (which I've done), but still can't delete the photo from it.

Any suggestions?

thanks!