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Comparing K to 10^3 and 10^-3 will tell you which direction the reaction proceeds to. Values in between these numbers do not indicate any strong favoring toward products not reactants, but can still tell you which reaction (forward or reverse) is happening -slightly- more. If K<0, the reactants are slightly favored and if K>0 the products are slightly favored.
To determine the direction of an equilibrium reaction you can just compare K to 1. If K <1, than the reaction favors the reactants and if K >1 then the reaction favors the products. Dr. Lavelle uses 10^3 or 10^-3 as comparison when he uses strongly favors. For example, if K<1, the reaction favors the reactants and if K < 10^-3, the reaction strongly favors the reactants. I hope this helps.
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