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Math Help - Compound Inequality

  1. #1
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    Compound Inequality

    If 3 < x < 4 then

    a. | x - 7 | < 3
    b. | x - 5 | < 2
    c. | x - 4 | < 3
    d. | x - 3 | < 4
    e. | x - 2 | < 5

    I need help solving this.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello baka

    Welcome to Math Help Forum!
    Quote Originally Posted by baka View Post
    If 3 < x < 4 then

    a. | x - 7 | < 3
    b. | x - 5 | < 2
    c. | x - 4 | < 3
    d. | x - 3 | < 4
    e. | x - 2 | < 5

    I need help solving this.
    Try giving x the values at the ends of the interval and see what happens. So:
    If x = 3:
    a. x-7 = -4 \Rightarrow |x-7| = 4

    b. x-5 =-2 \Rightarrow |x-2|= 2

    ... and so on.
    If x = 4:
    a. x-7 = -3\Rightarrow |x-7|=3

    b. x-5 =-1 \Rightarrow |x-2|= 1

    ... and so on.
    Can you see which of a to e will be correct? (There's more than one correct answer.)

    Grandad
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