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Homework Help: Solve this inequality

  1. Jan 24, 2010 #1
    6 - 4x (is more than or equal to) 2x - 3

    The answer to this inequality is:
    x is less than or equal to 1.5

    I got this far before getting stuck:

    add 3 to both sides:
    9 - 4x (is more than or equal to) 2x

    divide by 2:
    4.5 - 2x (is more than or equal to) x

    How do I finish this off?
     
  2. jcsd
  3. Jan 24, 2010 #2
    You know, you can just shift terms across the inequality as though its an ordinary equal sign (similar arithmetic rules apply!)
    So, try to make x the subject on one side, as though you are solving a simple equality equation!
     
  4. Jan 24, 2010 #3
    6 - 4x >= 2x - 3
    6 - 4x - 2x >= -3
    - 6x >= -3 - 6
    -6x >= -9
    x <= -9/-6
    x <= 1.5
     
  5. Jan 24, 2010 #4
    Thanks a lot guys! Just 1 more question.
    If x <= 1.5
    is it correct to say:
    -x >= -1.5
    In other words, does the <= invert when the figures involved go from negative to positive?
    Thanks again!
     
  6. Jan 24, 2010 #5

    Mark44

    Staff: Mentor

    The direction of the inequality changes when you multiply both sides by a negative number.
     
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