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I don't get when you use "or" or "and" in inequalities.

Like for this quadratic inequality:
x^(2) +x -12 > 0
becomes x < -4
x > 3

why is the answer {x|x<-4 or x>3} and not {x|3<x<-4} ?

  • Math -

    Your quadratic inequality has TWO solutions: x < -4 AND x > 3.

    The 2nd arrangement where you have x in the center of the inequality is normally used with compound inequalities.

  • Math -

    If you look at the graph, it would be clear that the part of the curve which is above the x-axis is in two separate parts, therefore the answer is
    x<-4 and x>3.
    On the other hand if the question had been x^(2) +x -12 < 0 , then the solution will be continuous on the number line, namely -4<x<3.

    See graph:

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