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Math Help - Why does this not work?

  1. #1
    Senior Member sakonpure6's Avatar
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    Why does this not work?

    we have the inequality x/(6x-9) <= 1/x , if we get rid of the denominators we get
    x^2 <= 6x-9 , x!= 3/2 and 0
    x^2-6x+9<=0
    (x-3)^2 <=0

    So the solution would be only at x=3. However the real solution includes 0<x<1.5 , but this does not work here? Now if we just subtract 1/x from x/(6x-9), it will give us the correct answer.

    What did I do wrong, am I missing something in my approach?
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  2. #2
    MHF Contributor
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    Re: Why does this not work?

    You need to remember that when you multiply or divide by negative numbers, the inequality sign changes its direction. So you will need to consider several different cases.
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  3. #3
    Senior Member sakonpure6's Avatar
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    Re: Why does this not work?

    Quote Originally Posted by Prove It View Post
    You need to remember that when you multiply or divide by negative numbers, the inequality sign changes its direction. So you will need to consider several different cases.
    but I did not multiply or divide by a negative number. So what gives?
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  4. #4
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    Re: Why does this not work?

    x is a VARIABLE, so it can take DIFFERENT values. There are some values of x where the denominator on the left (6x - 9) is negative, and obviously some values of x where the denominator on the right (x) is negative...
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