Rotated tires and noticed a bit of back and forth play in the rear diff, is that normal, if not what should I be checking for?

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2014 Chevy Silverado Crew Cab 5.3 Ecotec LTZ Z71 4x4
2012 Ford F-150 XLT EcoBoost 4x4
2007 Chevy Silverado 2500 HD D-Max 4x4
1996 Dodge Ram 1500 4x4 (just about dead)
2006 Jeep Liberty CRD

Are you referring to backlash or to the whole axle moving?

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2004 KJ 3.7 Limited:
IRO WJ Upper Arm -- WJ Rear LCA's -- Rear Driveshaft Spacer -- JBA Upper A Arms -- 4 inch Lift -- 265/75/16 4" B/S -- WasherBottle Relocate -- Custom High Mount Intake -- Carpet Delete -- Homebrew Winch Bumper -- Warn VR8000 -- Homemade Plow -- Pinch Weld POUNDED -- POR 15 inner fenders --

Some is normal. If you grab the drive line you might be able to feel the backlash, it shouldn't be much. Check, or drain your dif fluid right after driving it and if it comes out silvery, you've got problems. You can feel a clunk kind of like bad motor mounts (which these have every 50k miles or so) if it's getting really bad. But, if your fluid comes out looking good, and you're not getting a clunk back there, then I wouldn't worry. Crawl under any rear wheel drive vehicle of similar size for a rotation comparison of the driveline backlash might be worth looking at also.

transmission in neutral...

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05 CRD: H.D.S2 stat,WW Ironrock trilink&LCA's, OX rear,ARB front, 4.10's, ARB bumper, Suncoast,OME 3.5, JBA UCA,rock rails, Moabs&265/75 Duratracs, GDE tunes ,FFD fan,ARP's, 2 micron fuel, new valves,sasquatch battery tray & grid heater, tensioner relocated
Mech fan, VH & AC delete

The side to side movement.

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2014 Chevy Silverado Crew Cab 5.3 Ecotec LTZ Z71 4x4
2012 Ford F-150 XLT EcoBoost 4x4
2007 Chevy Silverado 2500 HD D-Max 4x4
1996 Dodge Ram 1500 4x4 (just about dead)
2006 Jeep Liberty CRD

rocking the tire side to side (checks the wheel bearings) or rotating the tire back and forth, like forward and reverse?

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05 CRD: H.D.S2 stat,WW Ironrock trilink&LCA's, OX rear,ARB front, 4.10's, ARB bumper, Suncoast,OME 3.5, JBA UCA,rock rails, Moabs&265/75 Duratracs, GDE tunes ,FFD fan,ARP's, 2 micron fuel, new valves,sasquatch battery tray & grid heater, tensioner relocated
Mech fan, VH & AC delete

If the whole axle moves more than it should, check your rear upper ubj and all your control arm bushings. If it's just one tire, check the wheel bearings, if it's both tires, check the diff

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2004 KJ 3.7 Limited:
IRO WJ Upper Arm -- WJ Rear LCA's -- Rear Driveshaft Spacer -- JBA Upper A Arms -- 4 inch Lift -- 265/75/16 4" B/S -- WasherBottle Relocate -- Custom High Mount Intake -- Carpet Delete -- Homebrew Winch Bumper -- Warn VR8000 -- Homemade Plow -- Pinch Weld POUNDED -- POR 15 inner fenders --

Oh and make sure your lug nuts are tight!

_________________
2004 KJ 3.7 Limited:
IRO WJ Upper Arm -- WJ Rear LCA's -- Rear Driveshaft Spacer -- JBA Upper A Arms -- 4 inch Lift -- 265/75/16 4" B/S -- WasherBottle Relocate -- Custom High Mount Intake -- Carpet Delete -- Homebrew Winch Bumper -- Warn VR8000 -- Homemade Plow -- Pinch Weld POUNDED -- POR 15 inner fenders --