Just bought a used 15 cherokee latitude 3.2l. I inflated all four tires to the same psi when the car has been sitting for couple hours, after driving about 5 to 10 minutes the sensor updated the tire pressure to the dash and the numbers are all same (35):

35 --- 35
| - - - |
35 --- 35

after about one and a half hour's high way driving, all four tires pressure went up unevenly, the front left tire went to 42, the front right and rear left when to 40, the rear right only went to 39 and at the end of the drive it finally went to 40:

42 --- 40
| - - - |
40 --- 39

There might be some reasons for that:
1. alignment issue, maybe the front left tire has more friction which caused a higher tire temperature so that the psi is higher.
2. Uneven tire weight caused by structure or driver? Since only one person sit in the car and above the front left side. BTW, I am only 120 lbs.
3. Cooling system exhaust heat to the front left side? Not really understand this.

Since I found the car draft to the left a little bit (only very few, I cannot even tell if the steering wheel is in the center or not), I the first reason may be the problem.

I would like to hear more about your driving experience, not sure this uneven tire pressure is normal.

 

If its pulling to the left even a little it can be alignment or maybe the brake is dragging on that wheel,Or even a unit bearing aka wheel bearing is not right on that wheel.But all that is a guess with out the jeep in front of me to look at things.Do you have any of the factory warranty left on it ?

 

Yes, it is still under factory warranty. I will certainly bring it to the dealer to have a check. Thank you for your reply.