Understanding Ksp

[LoLCareerGoals]

So can we say that Ksp is an inherent property of the given solute/solvent pair that doesn't change with changes in initial conditions and that those initial conditions only affect molar solubility?

I ran into that Ag2S is most soluble in question and still don't get a proper framework. I don't like intuitive answers until I can do a question formally in my sleep.
TBR's solution treats Ksp as a constant and compares 2 different "xs" to determine which is more soluble.
So Ksp is const no matter what (as long as temp is const) for a given solute - solvent?

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[polyatomic]

Yes.

Pretty much all K equilibrium constants (Keq, Ka, Ksp, Kb.....) stay constant as long as the temperature is constant.

When Berkeley compares the "x's" they're comparing the "molar solubility." Basically, that means the maximum number of moles that can be dissolved per liter of solution at which the solution becomes saturated. This is different from Ksp, the solubility constant, because Ksp represents an equilibrium constant. You always want to use the molar solubility (x) for calculating how much can dissolve into a solution.