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I am having difficulty understanding how my book came up with this answer.

Define $a \star b =ab+2b$, and suppose $x \star y = y \star x$. Then which of the following must be true?

A. $x+y=1$.

B. $y=0$.

C. $x=y$.

D. $x=-2$.

E. $xy=0$.

How did the text conclude that $x=y$ or C is the answer ?

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What does $x \star y$ mean in this context? – Old John Jul 11 '12 at 20:24
What are x,y, anyway? Real numbers? – DonAntonio Jul 11 '12 at 20:37
If $\star$ can be any operation, then the only condition that guarantees $x\star y = y\star x$ is $x=y$. But the question is not which condition guarantees the conclusion $x\star y = y\star x$, but rather, which condition is a necessary conclusion. Unless $\star$ is specified, nothing is a necessary conclusion of the condition. Are you sure they don't specify what $\star$ is, or give conditions that are satisfied by it? – Arturo Magidin Jul 11 '12 at 20:37
There are lots of possible answers depending on what it means. If we don't know which it is, I don't think we can be any help. Surely the text you found it from must explain somewhere?! – Old John Jul 11 '12 at 20:37
Sorry Let me re-edit my post – Rajeshwar Jul 11 '12 at 20:43
up vote 4 down vote accepted

Hint: So you are told that $xy+2y=yx+2x$. Cancel.

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We need the context to know what operation means $\star$, but i guess the equality $x=y$ must be true only if the operation $\star$ is a kind of operation such like division for example, that doesn't satisfy the conmutative property, and only in case that $x=y$ the equality $x \star y = y \star x$ is satisfied.

Sorry about my English, I hope you can understand me :D

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I think you will have to edit your answer to reflect the edited version of the OP's question. – M Turgeon Jul 16 '12 at 17:13

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