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いいえ
たとえばx<1/3とx>(-1)/(-3)は同値ではありません
x<1/3と同値なのはx<(-1)/(-3)です
右辺の分母分子に-を掛けただけで変形は完結しており、
両辺に負の値を掛けたわけではありません
だから、不等号の向きは変わりません
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ありがとうございます!