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Homework Help: Solving an inequality

  1. Mar 14, 2010 #1
    I am trying to find the domain of a square root function... To do so I have to solve the following inequality:


    1/(x+1) - 4/(x-2) >= 0

    This is how i attempted to solve it...:

    I crossmultilplied the denominator to get

    [(x-2) - 4(x+1)]/(x-2)(x+1) >= 0

    Multiplied both sides by (x-2)(x+1)

    (x-2) - 4(x+1) > = 0

    Expanded

    x - 2 -4x - 4 = 0

    -3x -6 >= 0

    -3(x+2) >= 0

    (x+2) <= 0 <---- at this point I am not sure if i swap the sign around, I haven't been taught inequalities before... but I will swap it around anyway.

    x <= -2

    Is this the correct answer? When I graph the entire function (sqrt of the above), I get part of the function less than -2 but also part greater than -2.... I dont really understand how there can be x > -2 if I got this restriction here of >-2.
     
  2. jcsd
  3. Mar 14, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    When dealing with an inequality, if you multiply by a negative number, the inequality changes.

    You can deal with this by multiplying by the square of the denominator

    i.e. ((x+1)(x-2))2
     
  4. Mar 17, 2010 #3
    Yeah, when I calculate it I get the same answer:

    x <= (-2)
     
  5. Mar 17, 2010 #4

    Mark44

    Staff: Mentor

    Just as rock.freak667 said, multiply both sides by (x+1)2(x-2)2. The domain is not just x <= -2.
     
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