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Thread: Interval Notation

  1. #1
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    Unhappy Interval Notation

    Need help on solving this absolute value inequality using interval notation!!

    2|x +6| + 4 > 1
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  2. #2
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    Quote Originally Posted by BadMaterial View Post
    Need help on solving this absolute value inequality using interval notation!!

    2|x +6| + 4 > 1
    This doesn't really make any sense...

    $\displaystyle |x + 6| \geq 0$ for all $\displaystyle x$.


    So that means that

    $\displaystyle 2|x + 6| \geq 0$ for all $\displaystyle x$

    $\displaystyle 2|x + 6| + 4 \geq 4$ for all $\displaystyle x$.


    Since it is always no less than 4, it must always be greater than 1...


    So $\displaystyle x \in (-\infty, \infty)$...
    Last edited by Prove It; Jan 10th 2010 at 05:28 PM.
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  3. #3
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    Quote Originally Posted by Prove It View Post

    $\displaystyle |x + 6| \geq 0$ for all $\displaystyle x$.


    So that means that

    $\displaystyle 2|x + 6| \geq 2$ for all $\displaystyle x$

    $\displaystyle 2|x + 6| + 4 \geq 6$ for all $\displaystyle x$.
    I think you meant to say

    $\displaystyle 2|x + 6| \geqslant 0$

    $\displaystyle 2|x + 6| + 4 \geqslant 4$

    (The result still remains true though BadMaterial)
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  4. #4
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    Thanks.

    Edited.
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