The discussion focuses on solving the inequality x^2 + 8x + 15 > 0 by factoring it into (x+5)(x+3) > 0. The solutions derived include x > -5 and x > -3 for the positive intervals, resulting in the final solution of (-∞, -5) ∪ (-3, +∞). The conversation highlights the time-consuming nature of this method and suggests that a more straightforward approach exists, emphasizing the importance of understanding the implications of the factors in the inequality.
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Physicsissuef said:Because you have two possible solutions for (x+5)(x+3)>0
the first one:
x+5>0 ; x>-5
x+3>0 ; x>-3
[tex](-5, +\propto) \cap (-3, +\propto) = (-3, +\propto)[/tex]
and the second
x+5<0 ; x<-5
x+3<0 ; x<-3
[tex](-\propto, -5) \cap (-\propto, -3) = (-\propto, -5)[/tex]
The final solution:
[tex](-\propto, -5) \cup (-3, +\propto)[/tex]
Anyway, this way is much more time-consuming... So you shouldn't use it in future.. There is much easier way...