The main problem is, in an explanation on a quiz or a test, I would have to relate a change in volume or pressure to Q or K (at least I think I would) and then use that as an explanation. Just saying "Le Chatelier's principle" and explaining what it is is not enough. I know what happens to K when heat is added, and I know the effect on Q when concentration is changed, but pressure and volume don't seem to directly affect either of those variables.
We can consider the shifting of the equilibrium position in the context of entropy, which, in this case, Gibbs energy, in where: ΔG = -RTInK (keeping in mind that, temperature is proportional to pressure and volume)
Considering the ratio of K, in the assumption of an equilibrium reaction where the forward reaction produces the product(s), the higher the value of K, the greater the relative concentration of the products. Hence, the lower the value of K, the lower the relative concentration of the products.
Which means, as the position of equilibrium shifts to the right according to the previously established premise, K > 1 and thus InK > 0, giving a negative value of ΔG. The opposite thus follows, whereby K < 1, InK < 0 and therefore ΔG is positive, favoring the reactants. The consideration of Gibbs energy is such that, if the value is too relatively extreme, then the position of equilibrium may be shifted so far out that relatively no reactions take place at all.
From ΔG = -RTInK and ΔG = ΔH - TΔS(sys)
-RTInK = ΔH - TΔS(sys)
InK = -(ΔH/RT) + (ΔS(sys)/R) in where RT = PV/n
Taking an exothermic reaction for the forward reaction, ΔH is negative, thus, -(ΔH/RT) is positive. Simply, as PV increases, RT increases and thus (ΔH/RT) decreases in magnitude, therefore, InK follows and K decreases in magnitude, favoring the reactants, as K is the ratio of the relative concentration of the products to the reactants.
Notice that, of a ratio of 0.999..., K < 1, InK < 0 and thus ΔG is positive, favoring the reactants as stated previously.And from this, we saw how in changing PV, K changes and in which also changes the position of equilibrium, as considered by ΔG.