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Because even though by adding the inert gas the pressure inside is increasing, the equilibrium constant is a ratio of the concentration of the products and reactants. The inert gas is not a product or reactant, and the moles and volume of the products and reactants are still the same. Concentration = moles/volume, therefore concentration for all the products and reactants are the same, which mean the equilibrium constant hasn't changed.
Inert gases usually won't react with reactants already present in the reaction, therefore, it will not change the concentration of the reactants nor products, and since the concentrations don't change, the equilibrium remains the same.
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