The hot water pressure is very low in the back part of the house. What do we need to check first?

First thing you should do is flush your water heater, you probably need to do that anyway. Second thing is remove and clean or replace aerators. Next thing is come back and tell us what you mean by "back of the house", one faucet, all faucets of one bath or what.

Harold suggested flushing your water heater. Let me show you how.
For long life and fewer troubles you should keep your heater clear of mineral build-up by FLUSHING NOT DRAINING on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures that are affected . Now pull each aerator and clean the screens. Be sure you put them back together the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps, Tom