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Homework Help: Probably a stupid question

  1. Nov 12, 2006 #1
    In interval notation, I was asked to solve for 5 < 2x - 1 ≤ 15

    I did this by making the 4 cases...

    2x-1>5 or 2x-1<-5 AND 2x-1≤ 15 and 2x-1≥-15
    x > 3 or x < -2 AND x ≤ 8 and x ≥ -7

    So for my final answer...i got [-7,-2),(3,8]

    But when i check it, none of the numbers between -7 and -2 check...what'd I do wrong?

    Lastly, is the answer actually just (3,8]?
  2. jcsd
  3. Nov 12, 2006 #2
    What's the use in checking if 2x-1<-5 and 2x-1>= -15?
  4. Nov 12, 2006 #3
    honestly...I have no idea, but we were taught to make four cases for those...so that's how i've been doing it ever since.
  5. Nov 12, 2006 #4
    Actually, I just realized that I could've solved for x by adding 1 to the left and right, and dividing by 2 to the left and right...which gives me an answer of 3 < x ≤ 8...i'm pretty sure that's right...guess i went about it the wrong way
  6. Nov 12, 2006 #5
    Yup, that's probably the easiest way.
  7. Nov 12, 2006 #6

    James R

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    Homework Helper
    Gold Member

    You're probably confusing it with a problem like:

    [tex]2 < |2x - 1| \le 15[/tex]

    where the absolute value sign creates a problem.
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