A loopback plug is a diagnostic tool used to test the functionality of network interfaces by creating a signal loop. In this case, since the user's device is hardwired to the network but cannot access the internet, using a loopback plug can help determine whether the issue is with the network interface card (NIC) or the Ethernet cable.

This is an example of a public IP address that can be assigned by an ISP to a router's WAN (Wide Area Network) port. A public IP address is a globally unique and routable address that allows a device to communicate with other devices on the internet. A private IP address, such as
10.1.50.30 or 172.22.40.6, is a non-routable address that is used within a local network and cannot be directly accessed from the internet. A link-local IP address, such as 169.254.168.10, is a self-assigned address that is used when a device cannot obtain a valid IP address from a DHCP server.

The "Out of Range" message typically indicates that the resolution being sent by the laptop is not supported by the projector. Changing the resolution settings on the laptop to match the supported resolution of the projector is the most immediate and relevant action to address this issue.

SODIMM stands for Small Outline Dual In-line Memory Module and is a type of memory module that is compatible with laptops and other small devices. SODIMMs are smaller and thinner than DIMMs (Dual In-line Memory Modules), which are typically used for desktop PCs and servers.
Upgrading or adding SODIMMs can increase the amount of RAM available for a laptop, which can improve its performance and speed when running process-intensive tasks.