When i brake sometimes my wheel moves back and forth- is this from the balancing of the tires.?

 

You would need to check the runout (trueness) of your rotor w/hub, wheel, and tire. You should also do a complete front end inspection with those symptoms to check for worn parts with play.

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2000 F-150 XL, RC, LB, 5.4L, 4R70W, 4.10LS,
Class III tow, Payload #3, & Convenience pkgs.,
4-wheel disc/ABS, Chestnut/Parchment 40/60,
Ford bedliner w/Paintsaver & gas/wheel/spare locks,
K&N F.I.P.K. w/Outwears pre-filter, Superchip,
Dynomax ultra-flow welded 3" cat-back w/ 3" Y-pipe,
Hellwig front & rear anti-sway bars, Rancho RS 9000s,
Pirelli Scorpion Zero 275/60/16s, Mobil 1, K&N oil filter.