Question 340408
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If the endpoint is included, then you use [ or ].  If the endpoint is not included you use ( or ).  When one of the endpoints is infinity, you ALWAYS use ( or ) for the unbounded side.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ <\ 5\ -\ 2x]


Add -5 to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5\ <\ -2x]


Multiply both sides by *[tex \Large -\frac{1}{2}].  Since you are multiplying by a negative, reverse the sense of the inequality.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{2}\ >\ x]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ < \frac{5}{2}]


So there is no lower bound and the upper bound is *[tex \Large \frac{5}{2}]


Note that your inequality symbol is strictly less than, hence the upper bound endpoint is NOT included.  The interval is thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(-\infty,\frac{5}{2}\right)]


Contrast this with the similar situation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ 5\ -\ 2x]


which would be solve in precisely the same way, but the result WOULD include the upper bound endpoint, thus:


*[tex \Large \ \ \ \ \ \ \ \ \ \ \left(-\infty,\frac{5}{2}]<font size="+5">]</font>



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