Question 497016
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You can tell your teacher thank you very much for the answer -7, but that is only one element of the solution set of your inequality that has infinite elements.


If *[tex \Large 8b\ +\ 9\ \geq\ 0\ \ ] then *[tex \Large |8b\ +\ 9|\ =\ 8b\ +\ 9\ \ ], hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8b\ +\ 9\ <\ 63]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8b\ <\ 54]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ <\ \frac{27}{4}]


On the other hand, if *[tex \Large 8b\ +\ 9\ <\ 0\ \ ] then *[tex \Large |8b\ +\ 9|\ =\ -8b\ -\ 9\ \ ], hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -8b\ -\ 9\ <\ 63]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -8b\ <\ 72]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ >\ -9]


Hence the solution set is


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \{b\,|\,b\,\in\,\mathbb{R},\,-9\,<\,b\,\frac{27}{4}\}]


-7 is an element of this set, but hardly descriptive of the solution.


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