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to cut into (a line, conversation, etc.); to force oneself into (e.g. a crowd); to wedge oneself into; to squeeze oneself into; to intrude on; to interrupt
to fall below (of stock prices, sales, etc.); to drop below
行列に割りこむ人がいて周囲が怒っていた。
Someone cut in line and the people around were angry.
会話に割りこむのは失礼だと注意された。
I was told that interrupting a conversation is rude.
競合他社が市場に割りこんできた。
A competing company has broken into the market.