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to mutter; to murmur; to grumble
to tweet; to post on Twitter
彼は不満そうに何かをつぶやいて席を立った。
He muttered something with displeasure and left his seat.
独り言をつぶやく癖があるので周囲に驚かれる。
I have a habit of muttering to myself, which startles those around me.
祖母は祈りの言葉を小さくつぶやいていた。
My grandmother was quietly murmuring words of prayer.