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Doubt in an inequality problem

  1. Dec 1, 2016 #1
    1. The problem statement, all variables and given/known data
    Given : (y+2)(y-3) <= 0

    2. Relevant equations

    3. The attempt at a solution
    Now, I have y-3 <= 0 or y+2 <= 0
    Hence, y <= 3 or y <= -2
    But how
    is correct?
    I think
    is wrong because y <= -2.
    Can someone please clarify?
  2. jcsd
  3. Dec 1, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You could draw a graph of ##(y+2)(y-3)## to see what's happening.

    What happens if both ##y+2 < 0## and ##y-3 < 0##?
  4. Dec 1, 2016 #3
    In that case , we will keep y < -2 and ignore y < 3.
    I think I got it. We have to ignore y+2 <= 0 and y-3 >=0 as
    is not possible and keep
    Thanks PeroK :)

    Attached Files:

  5. Dec 1, 2016 #4


    Staff: Mentor

    No, the above doesn't follow from the inequality. I think you might already have solved this inequality, but showing where you went wrong is worthwhile.
    For the product of two expressions to be negative, one of them has to be negative, and the other has to be positive. Since this can happen in either of two ways, you need to examine two different cases.
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