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Math Help - Rational inequality

  1. #1
    Junior Member
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    Rational inequality

    Please check my answers:

    Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.

    7. (x-5)/(x+2)>0
    this is what I got:

    x-5=0 or x+2=0
    (I added 5) (I subtracted 2)

    got: 5>0 or -2>0

    graph (-∞, -2) or (5, ∞)


    8. (-x+8)/(x-3) > or equal to 0
    this is what I got:

    -x+8 = 0 x-3=0
    (I subtracted 8, then divided by -1) (I added 3)

    I then got x=8 x=3

    graph: (3, 8]



    9. (2)/(x-2) < 1 (I wasnt too sure how to do this one)
    graph: (2, 4)


    10. (10-2x)/(4x+5)< or equal to
    this is what I got:

    10x-2x=0
    I subtracted 10, then divided by -2x and x=5

    4x+5=0
    I subtracted 5, then divided by 4x, and x= -5/4

    graph: (-∞, -5/4) or [5, ∞)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by soly_sol View Post
    Please check my answers:

    Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.

    7. (x-5)/(x+2)>0
    this is what I got:

    x-5=0 or x+2=0
    (I added 5) (I subtracted 2)

    got: 5>0 or -2>0

    graph (-∞, -2) or (5, ∞)
    Your given answer does not agree with the diagram. You should have

    x>5 or x<-2

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by soly_sol View Post
    8. (-x+8)/(x-3) > or equal to 0
    this is what I got:

    -x+8 = 0 x-3=0
    (I subtracted 8, then divided by -1) (I added 3)

    I then got x=8 x=3

    graph: (3, 8]
    The equality holds when x=8, and the expression changes sign also at x=3
    also at x=5 the expression is positive so the inequality holds when:

    x<=8, and x>3, which is the interval (3,8].

    RonL
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