Question 1119618
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Consider the right-hand inequality.


If *[tex \Large x\ <\ 1] then *[tex \Large \{x\ <\ 1\ \in\ \mathbb{R}\ |\ 5\ <\ \frac{1}{x\ -\ 1}\}\ =\ \empty] because 5 cannot be smaller than any negative number.


If *[tex \Large x\ >\ 1] then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5x\ -\ 5\ <\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ <\ \frac{6}{5}]


Hence, *[tex \Large 1\ <\ x\ <\ \frac{6}{5}]


And since the entirety of that interval is less than 5, the entire trichotomy is satisfied by this open interval.

								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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