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If you are using RHEL/CentOS 7 (the OP was not, but I thought I'd share the solution for my case), then you will need to use firewalld instead of the iptables service mentioned in other answers.

firewall-cmd --zone=public --add-port=80/tcp --permanent firewall-cmd --reload

And then check that it is running with:

firewall-cmd --permanent --zone=public --list-all

It should list 80/tcp under ports