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Homework Help: Solve inequality

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve the inequality and write your answer in interval form.

    2x+1 <= 5- x < x-7


    3. The attempt at a solution

    fist part 2x+1 <= 5- x
    -4 <= -x
    4 >= x

    second part

    5- x < x-7
    0<-12 ,,,,,,,,,, O,O how it's gone be like this ?

    well if it's right how i can write it in interval form ?
     
  2. jcsd
  3. Mar 14, 2010 #2

    tiny-tim

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    Hi MrNeWBiE :smile:

    (have a ≤ :wink:)
    No, both these are wrong, for the same reason:

    when you transfer -x across an = or ≤, you must multiply it by -1.
     
  4. Mar 14, 2010 #3
    ohhhh i see it now ,,,

    2x+1 ≤ 5- x

    -4≤-3x

    x≤4/3

    5- x < x-7
    -2x<-12 .....x>6

    now they are right ?

    yet i didn't understand you ,,,,,
     
  5. Mar 14, 2010 #4

    tiny-tim

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    Yup! :biggrin:

    (I just meant that when you move -x across, it becomes +x, as you've done)

    And now express that it interval form (you may need to use ∞). :wink:
     
  6. Mar 14, 2010 #5
    (-∞,4/3]U[4/3,6) right ,,, ? or it's to ∞ not 6 ...
     
  7. Mar 14, 2010 #6

    tiny-tim

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    That's just (-∞,6) :rolleyes:
    and that's (-∞,∞). :smile:
     
  8. Mar 14, 2010 #7
    i know that ,,,

    but our tacher keep asking for more details ,,,,

    if i write like this " (-∞,6) " he will say where is the 4/3 and the same for the other ,,, >.<
     
  9. Mar 14, 2010 #8

    tiny-tim

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    Yes, and that's because (-∞,6) is wrong!

    Go back to x≤4/3

    .....x>6.
     
  10. Mar 14, 2010 #9
    x>6 how it's gone be x≤4/3 ,,,

    isn't 6>4/3 ,,,=p

    how x > 6 then x≤4/3 ??
     
  11. Mar 14, 2010 #10

    tiny-tim

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    Exactly!

    So that means … ? :smile:
     
  12. Mar 14, 2010 #11
    no answers maybe ...
     
  13. Mar 14, 2010 #12

    tiny-tim

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    Looks like it! :smile:
     
  14. Mar 14, 2010 #13
    thx xD

    sorry for wasting your time
     
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