To summarize my discussion with the poster :

While using TV as an extended desktop is easy for Windows 8.1/10, Mac and Android, it is not that easy on Linux.

Below are some directions you could follow :

• Connect the TV to the computer via HDMI, using one of the numerous hardware solutions for HDMI extender cables (example), or HDMI over IP (example) or over Wireless. These solutions can extend reception up to more than a hundred meters.
• Connect your tablet as secondary monitor and cast it to the TV. Numerous sources exist for this and here is one random link.

These all require new hardware to be bought. As you know best your budget and physical constraints, you will need to do the required research and decide. If you have good electronics shops in your area, choose one that allows returns, or use Amazon, so you could backtrack.