delete all text messages on ios 7.1.2

I have an iphone 4 that we just updated to iOS 7.1.2 (I know, behind the times!). I need to delete thousands of texts hogging my memory, all at once. I googled it and found a way to do it through Settings on iOS 8, but I can't find that on 7.1.2. Does anyone know how?

Currently, my message box has "Edit" at top left, but when I press it, it simply gives me options to delete one message stream at a time.

Thanks for the help.

Sincerely, Jeremy