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Given inequality is:
15 < 3(x-2)/5 < 0
=> 15*5 < 3(x-2) < 0*5
=> 75 < 3(x-2) < 0
=> 75/3 < x-2 < 0
=> 25 < x-2 < 0
=> 25 +2 < x <0+2
=> 27 < x < 2