Question 182584
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*[tex \LARGE \text{          }\math 4 |x + 4| - 1 < 6]


*[tex \LARGE \text{          }\math 4 |x + 4|  < 7]


*[tex \LARGE \text{          }\math |x + 4|  < \frac{7}{4}]


*[tex \LARGE \text{          }\math |w| < z \ \ \Rightarrow\ \ w < z \text{ or }\math -w < z], so:


*[tex \LARGE \text{          }\math x + 4 < \frac{7}{4}\ \ \Rightarrow\ \ x < \frac{7}{4} - 4 = \frac{-9}{4}], or


*[tex \LARGE \text{          }\math -(x + 4)  < \frac{7}{4}\ \ \Rightarrow\ \ -x < \frac{7}{4} + 4 \ \ \Rightarrow\ \ -x < \frac{23}{4} \ \ \Rightarrow\ \ x > \frac{-23}{4}]


(Note the sense change on the inequality after multiplying by -1)


Therefore the solution set interval is 


*[tex \LARGE \text{          }\math \left( -\frac{23}{4}, -\frac{9}{4}\right)]


Notice that the interval endpoints are indicated with parentheses rather than square brackets.  The original inequality symbol was < rather than *[tex \Large \leq] meaning the endpoints are excluded. 




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