Here's how to write the balanced equation for the reaction of silver nitrate (AgNO₃) and magnesium bromide (MgBr₂) to form silver bromide (AgBr) and magnesium nitrate (Mg(NO₃)₂):

Unbalanced Equation:

AgNO₃ + MgBr₂ → AgBr + Mg(NO₃)₂

Balancing the Equation:

1. Silver (Ag): There is one Ag on each side, so it's balanced.

2. Nitrate (NO₃): There is one NO₃ on the left and two NO₃ on the right. To balance, put a coefficient of 2 in front of AgNO₃.

3. Magnesium (Mg): There is one Mg on each side, so it's balanced.

4. Bromide (Br): There are two Br on the left and one Br on the right. To balance, put a coefficient of 2 in front of AgBr.

Balanced Equation:

2 AgNO₃ + MgBr₂ → 2 AgBr + Mg(NO₃)₂