How do you balance #Al + N_2 -> AlN#?
Use a non-integral coefficient.
Is this equation balanced? How do you know? Of course, your teacher might want you to use integral coefficients. The point is that while I cannot have half a molecule of dinitrogen, I can certainly have 14 g dinitrogen, i.e. half a mole. The stoichiometry will be the same in either case.
Could I multiply each side of the equation by 2? Would this change the stoichiometry? Note that the use of 1/2 coefficients has long precedent when solving stoichiometric problems.