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Absolute value inequality

  1. Nov 7, 2014 #1
    • Member warned about not using the homework template
    Question:
    True or False If x^2<4 then |x|<=2

    My solution:
    I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.
     
    Last edited by a moderator: Nov 7, 2014
  2. jcsd
  3. Nov 7, 2014 #2

    Mark44

    Staff: Mentor

    x2 < 4 is equivalent to -2 < x < 2 or |x| < 2. What the text has appears to be a typo.
     
  4. Nov 7, 2014 #3

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It's probably a typo, although logically it is true:

    If ##x^2 < 4## then ##|x| < 2## hence ##|x| \le 2##

    If it were false, then there would be ##x## with ##|x| > 2## yet ##x^2 < 4##
     
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