The solution is x = 5 (mod 7).


Because 6x = 6*5 = 30 gives the remainder 2 when divided by 7.


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In other words, in the ring (in the field !) of integers (mod 7) the solution to the equation

    6x = 5 (mod 7) 

is 

    x = 5 (mod 7).



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Or, in the multiplicative group of integers (mod 7) the solution to the equation

    6x = 5 (mod 7) 

is 

    x = 5 (mod 7).



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Or, in the additive group of integers (mod 7) the solution to the equation

    6x = 5 (mod 7) 

is 

    x = 5 (mod 7).