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Teacher told to set absolute value inequality to equal 0

  1. Mar 25, 2015 #1
    So I was helping my sister on homework and there was this problem:
    2 abs(2x + 4) +1 > or equal to -3
    teacher told her to ignore the -3 and just set it equal to zero.
    Soo should you? This question got me confused. can't you just go about solving, bringing the 1 to the left and then dividing by 2?
    EDIT: when I do it I get interval notaion from -3 to 3
    and with the zero thing i get -2.5 to 2.5
     
    Last edited: Mar 25, 2015
  2. jcsd
  3. Mar 25, 2015 #2

    Mark44

    Staff: Mentor

    ##2|2x + 4| + 1 \ge -3##
    ##\Leftrightarrow 2|2x + 4| \ge -4##
    ##\Leftrightarrow |2x + 4| \ge -2##
    Since the absolute value is always greater than or equal to zero, you can change the last inequality to ##|2x + 4| \ge 0##.
     
  4. Mar 25, 2015 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    |anything|≥0. Therefore 2|2x+4|+1≥1 for all x. Any x will do.
     
  5. Mar 25, 2015 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Your teacher's point is that "f(x)= 0", for f a continuous function, is the boundary beween "f(x)> 0" and "f(x)< 0".
     
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