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Math Help - Express an interval with an absolute value

  1. #1
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    Express an interval with an absolute value

    I am looking at a problem in a review of basic set notation which reads as follows:

    (a) [1, 5]
    (b) (1, 4)
    (c) [-1, 6)
    (d) [-4, 4]

    The interval in (d) may be expressed in the form {x | x is a number and |x| ≤ 4}. Two of the other intervals listed can similarly be expressed with the aid of absolute values. Find the two and display the result.


    I assume the intervals you could do this with would be (a) and (b), but I don't really know where to go from there. Could anyone offer any hints in the right direction? Thanks!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Express an interval with an absolute value

    Quote Originally Posted by Ragnarok View Post
    I am looking at a problem in a review of basic set notation which reads as follows:

    (a) [1, 5]
    (b) (1, 4)
    (c) [-1, 6)
    (d) [-4, 4]

    The interval in (d) may be expressed in the form {x | x is a number and |x| ≤ 4}. Two of the other intervals listed can similarly be expressed with the aid of absolute values. Find the two and display the result.


    I assume the intervals you could do this with would be (a) and (b), but I don't really know where to go from there. Could anyone offer any hints in the right direction? Thanks!
    The interval in (a) may be expressed in the form {x | x is a number and |x-3| ≤ 2}.

    The interval in (b) may be expressed in the form {x | x is a number and |x-5/2| < 3/2}.
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  3. #3
    Member kalyanram's Avatar
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    Re: Express an interval with an absolute value

    In general
    c \leq x \leq d \equiv |x-a| \leq b \equiv a-b \leq x \leq a+b \implies a= \frac{c+d}{2} , b = \frac{d-c}{2}

    Regards,
    Kalyan
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