Introduction of inert gas (at the same temperature) will affect the equilibrium if :

volume is constant and ${\mathrm{\Delta n}}_{\mathrm{g}}=0$

pressure is constant and ${\mathrm{\Delta n}}_{\mathrm{g}}=0$

pressure is constant and ${\mathrm{\Delta n}}_{\mathrm{g}}\ne 0$

volume is constant and ${\mathrm{\Delta n}}_{\mathrm{g}}\ne 0$