If x and y are real numbers,which of the foll | vedclass

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(C) By the triangle inequality for absolute values,we have the property: $||x| - |y|| \leq |x - y| \leq |x| + |y|$.Specifically,the identity $|x - y|

Vedclass · Accepted Answer

$|x - y| = ||x| - |y||$

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(C) By the triangle inequality for absolute values,we have the property: $||x| - |y|| \leq |x - y| \leq |x| + |y|$.Specifically,the identity $|x - y| = ||x| - |y||$ is not always true for all real $x$ and $y$.However,checking the standard properties of absolute values:$1$. $|x + y| \leq |x| + |y|$$2$. $|x - y| \geq ||x| - |y||$Looking at the options provided,none of the equalities are universally true for all real $x$ and $y$. However,in many textbook contexts,the question likely intends to test the reverse triangle inequality property: $||x| - |y|| \leq |x - y|$.Given the standard form of such questions,if we assume the question implies which inequality holds or is a standard identity,there might be a typo in the options. But strictly mathematically,none of the equalities $A, B, C, D$ are identities. If we must choose the most 'standard' related property,$C$ is often discussed as the lower bound.

If $x$ and $y$ are real numbers,which of the following is always true?

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