Here's how to write the balanced chemical equation for the reaction of solid sodium bromide with chlorine gas to produce solid sodium chloride and bromine gas:

Unbalanced Equation:

NaBr(s) + Cl₂(g) → NaCl(s) + Br₂(g)

Balancing the Equation:

* Sodium (Na): There's one sodium atom on each side, so it's balanced.

* Bromine (Br): There's one bromine atom on the left and two on the right. We need to add a coefficient of 2 in front of NaBr.

* Chlorine (Cl): There are two chlorine atoms on the left and one on the right. We need to add a coefficient of 2 in front of NaCl.

Balanced Equation:

2NaBr(s) + Cl₂(g) → 2NaCl(s) + Br₂(g)