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If the concentration of a reactant is increased, the reaction should typically proceed to the right (towards products). If the concentration of the products is increased, then typically the reaction will proceed in the reverse direction, towards the left (towards reactants).
If the concentration of molecules on one side of a reaction increases, then the reaction will proceed in the direction that would produce the molecules on the other side of the reaction in order to consume the excess and so as to reach equilibrium again. Thus if the concentration of reactants increases, then the forward reaction would be favored because more product would be produced until the ratio of products to reactants equals the equilibrium constant. If the concentration of products increases, then the reverse reaction will be favored because the concentration of reactants will increase until the ratios are at equilibrium.
So the whole concept of Le Chatelier's principle is that you are trying to minimize the effect of some sort of strain you have put on the system. To answer what you're saying, if the concentration of the reactants goes up, then that means you are adding more reactants to the system at equilibrium, so the system is going to use up more of the reactants to get back to equilibrium, so the reaction will shift to the right (towards the product). This makes sense mathematically, the equilibrium constant for the reaction must stay the same, and it equals to the concentration of products over the concentration of the reactants, so if the concentration of the reactants goes up, then the concentration of the products must go up as well. The same concept for increasing the concentration of products at the beginning, just the opposite of everything I have already said.
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