You can increase/decrease the volume and keep the pressure constant, and thus temperature has to increase/decrease, or you can keep the temperature constant and the pressure has to increase/decrease. You can increase/decrease pressure and keep volume constant, and so temperature has to increase/decrease.
And every other possible combination you can think of.
The left side has to be equal to the right side is all.
R does not change, and it would make things pretty complicated to change n too much.
What are the assumptions in an ideal gas?