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$AlBr_3 + Cl_2 -> AlCl_3 + Br_2$
Balance Cl and Br by adding atoms
$AlBr_3 + 3/2Cl_2 -> AlCl_3 + 3/2Br_2$
Multiply by 2 to get to the nearest whole number
$2AlBr_3 + 3Cl_2 -> 2AlCl_3 + 3Br_2$

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