Question 184416
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ |2x -4| < 10]


Means:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ 2x -4 < 10 \ \ \Rightarrow\ \ 2x < 14 \ \ \Rightarrow\ \ x < 7]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ -(2x -4) < 10\ \ \Rightarrow\ \ -2x < 6 \ \ \Rightarrow\ \ x > -3]


Note change of inequality sense when multiplying by *[tex \Large -\frac{1}{2}].


So your interval is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ -3 < x < 7]


In interval notation: (-3,7).  Note use of parentheses vice square brackets because equals was not included in the original inequality relationship.


You can draw your own graph.  Remember to use open circles on the endpoints.


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