adjective
Mutual is an adjective that describes something that is shared or experienced by two or more parties.
adverb
Mutually is the adverb form of mutual, used to describe actions done in a shared or reciprocal manner.
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The business partners had a mutual agreement to split the profits evenly.
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We have a mutual understanding that we'll always have each other's backs.
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Me and my best friend have a mutual vibe that no one else understands.
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The mutual respect between the two leaders paved the way for successful negotiations.