Why can't I text certain people from my iPhone 5s?

I

iMore Question

I purchased an iPhone 5s (second hand) last July. Everything works fine, except when I attempt to text a certain few numbers. I type out the message and click send and after 1-2 seconds, it says the message was 'Not Delivered'. I have tried everything to resolve this issue, from deleting and re-creating the contact(s), restarting my phone, typing in the number(s) manually instead of selecting it from the phonebook, but to no avail. Can anyone help me resolve this? iMessage works, but not regular text messaging and I have topped up my credit, so that's not the reason either.
Thanks in advance!
 

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