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Thread: What is the difference between... these two intervals

  1. #1
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    What is the difference between... these two intervals

    When dealing with inequalities like this What is the difference between... these two intervals-union.jpg, What is the difference between... these two intervals-answer.jpg The problem states that I need to write the given set as an interval or a union of two intervals. Are the answers above both correct? Click image to enlarge please.
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  2. #2
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    Re: What is the difference between... these two intervals

    Hello, Eraser147!

    When dealing with inequalities like this: .$\displaystyle |x+4| \:<\:\tfrac{1}{200}$

    The problem states that I need to write the given set as an interval or a union of two intervals.

    Are both these answers correct?

    . . $\displaystyle \left(-\tfrac{801}{200},\,-\tfrac{799}{200}\right)$ . . . . $\displaystyle \left(-\infty,\,-\tfrac{801}{200}\right) \:\cup\:\left(-\tfrac{799}{200},\,\infty\right)$

    Obviously, both of them cannot be correct.

    Here is helpful rule.

    We have an inequality with an absolute value.

    If the inequality is "less than", $\displaystyle |x| \:{\color{red}{<}}\: a$
    . . then $\displaystyle x$ is between $\displaystyle \text{-}a$ and $\displaystyle +a$.
    This is written: .$\displaystyle \text{-}a \,<\,x\,<\,a$

    If the inequality is "greater than", $\displaystyle |x|\:{\color{red}{>}}\:a$
    . . then $\displaystyle x$ is "outside" of $\displaystyle \text{-}a$ and $\displaystyle +a$.
    This is written: .$\displaystyle x\,<\,\text{-}a\;\cup\;x\,>\,a$

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  3. #3
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    Re: What is the difference between... these two intervals

    Very helpful, thank you very much.
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