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# Non-Commutative Operation

Pro Problems > Math > Number and Quantity > Number Theory > Star Operations

## Non-Commutative Operation

If the operation a ♦ b is defined as follows: a ♦ b =
a
b
+ a, find the value of x such that:

x  ♦ 2x = 2x ♦ x.

Note that this operation is not commutative; the order of operands cannot be exchanged without altering the result of the operation.

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Problem by Mr. Twitchell

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