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modulus inequality

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    | 4-x^2 | < 3

    i know that this means |4-x^2| <± 3 and can solve it to get x>± sqrt7 and x>±1

    the answer wants -sqrt7<x<-1 and 1<x<sqrt7

    can somebody explain this for me please? thanks
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    (Original post by rub em out)
    | 4-x^2 | < 3

    i know that this means |4-x^2| <± 3 and can solve it to get x>± sqrt7 and x>±1

    the answer wants -sqrt7<x<-1 and 1<x<sqrt7

    can somebody explain this for me please? thanks
    You should find a graph useful
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    You can break it up in to 2 inequalities, i.e:
    4 - x^2 < 3 [1]
    4 - x^3 > -3 [2]

    Then for [1]
    x^2 > 1
    And this is only satisfied when |x| > 1, I.E. x > 1 and x < -1
    [2] is similar.
    Spoiler:
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    Note this may not be the best (or even correct) way of approaching this
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    (Original post by steve2005)
    You should find a graph useful
    that was useful! picturing it like that definitely helps thankyou!

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