Question 213901
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Assume that the two expressions are equal:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x + 4\ =\ x - 4]


Add *[tex \LARGE -x] and -4 to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x + 4 - x - 4\ =\ x - 4 - x - 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ =\ -8]


This absurd result proves that the opposite case of your initial assumption is false, therefore *[tex \LARGE x + 4] and *[tex \LARGE x - 4] are NEVER equal.  Another way to look at it is to say <i>if</i> *[tex \LARGE x + 4] and *[tex \LARGE x - 4] are equal, <i>then</i> for every real number *[tex \LARGE x], *[tex \LARGE 0\ =\ -8], but since *[tex \LARGE 0\ \neq\ -8], there is no value of *[tex \LARGE x] for which *[tex \LARGE x + 4] and *[tex \LARGE x - 4] are equal.


You should be able to come up with your own examples.  Picking a few numbers to substitute is all you have to do.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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