Your Internet service provider will assign a unique ip address to every client that purchases internet through them. This ip address is assigned to your house/apartment. Your house has one ip address. Inside of your house, you have a router. This assigns local ip addresses to each device connected to your internet connection. These ip addresses are private, and not visible to Jagex. The ip address of your apartment is what jagex is concerned with. Which is just one, unique ip address. 

You can just unplug your modem and router and wait like two minutes and your router will be assigned a new i.p. address

 

 

This would assign a new local ip address. His public IP address assigned by his ISP would remain the same. 

 

In the OP he states that he's using his friends and his own ISP, so they should both be different IP addresses, unless he's not using his friends.

 

Anyways, my accounts ranged from 6 months old to a 3 days old.

 

Yea, if hes using his friends internet, they would be different ip addresses. 

IP Adresses are different on each connection (wi-fi, etc).

IP Adresses are different on each connection (wi-fi, etc).

 

Uh, no.

 

My LAN and Wifi have the same IP.