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Inert gases do no side reactions because they're inert. Although they changed the pressure (PV = nRT), they don't change the volume of the container used and thusly the concentrations (n/V) are still the same. This is true for partial pressures as well, since the volume is constant and the moles of gas of the reactants/products are the same. If pressure was changed via changing volume, then values of partial pressures, and concentrations change, and thus reaction quotients (Q) change.
The equilibrium constant does not change when pressure is increased by adding an inert gas because it does not react with anything in the reaction. The concentration of each reactant are not changed. The system will still be at equilibrium, which leaves K to remain the same.
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