If a stimulus opens ligand-gated sodium ion channels, the neuron will

The neuron will depolarize, if a stimulus opens ligand-gated sodium ion channels. Depolarize in other words is to remove or reduce the polarization of, also to cause to become partially or wholly unpolarized. If a stimulus will open ligand-gated sodium ion channels, the neuron will depolarize.

Well for any equation if all the coefficients are set to 1, this might result in unequal numbers of atoms of the same element on both sides

Explanation:

For example:

(for this equation all the coefficient (the number before element) are 1 but you can clearly see it is not balanced because one side has 1 A atom and other side has 2 B atoms....therefore we need to balance em.

Here both atoms are balanced.