How to delete photos from the Photo Album and Photo Stream from an iPhone?

I've been having this problem with the Photo Album and Photo Stream for a while now and I don't know how to delete them. I tried to look for a delete button, but the only options I got is either to Share or to Add To. I don't want those photos and I need help. I even called Apple Support and they didn't help at all. And I do t want to reset my phone. What do I do without having to delete all my information or photos?

You can delete pictures in Photo Stream by going to the Photo Stream tab on the bottom and clicking edit (The select pictures, then delete) or the trashcan button on a selected picture. And you can't delete pictures in the photo album because that is where all the pictures go. You have to go to the Photo Stream tab or the Camera Roll or where ever its from to delete them.