In a manner that is capable of change; in a way that is subject to alteration or variation.
From 'changeable' plus '-ly' suffix (from Old English '-lice'). The '-ly' suffix converts adjectives to adverbs, modifying how an action or state occurs.
Most English adverbs ending in '-ably' are quite rare in everyday speech—'changeably,' 'culpably,' 'advisably'—because we prefer simpler ways to express these ideas, making academic and formal writing the last refuge for these fancy adverbs.
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