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Math Help - Solving Rational Inequalities

  1. #1
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    Solving Rational Inequalities

    Solve this inequality: 5/6x+2/3x>3/4.
    So I simplified the left side and got 3/2x, then moved the equation to one side and got 3/2x-3/4>0. I got x>1/2, but the answer is wrong.
    Can somebody help me?

    Thanks in advance.
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  2. #2
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    Re: Solving Rational Inequalities

    Lets see your work. How did you get x>1/2 , from 3/2x-3/4>0 ?
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  3. #3
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    Re: Solving Rational Inequalities

    3/2x>3/4. Then, I divided both sides by 3/2.
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  4. #4
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    Re: Solving Rational Inequalities

    That gives (1/x) > (1/2) .
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  5. #5
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    Re: Solving Rational Inequalities

    How did you get that?
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  6. #6
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    Re: Solving Rational Inequalities

    Using algebra ... and assuming what you meant was 3/(2x) > 3/4 .

    Was the original problem: Solve 5/(6x) + 2/(3x) > 3/4 ?
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  7. #7
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    Re: Solving Rational Inequalities

    Yes
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  8. #8
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    Re: Solving Rational Inequalities

    Quote Originally Posted by SammyS View Post
    Using algebra ... and assuming what you meant was 3/(2x) > 3/4 .

    Was the original problem: Solve 5/(6x) + 2/(3x) > 3/4 ?
    Quote Originally Posted by Dragon08 View Post
    Yes
    Starting with     \frac{3}{2x}>\frac{3}{4}

    Multiply by 2/3    \frac{2}{3}\cdot\frac{3}{2x}>\frac{2}{3}\cdot\frac  {3}{4}

    This gives       \frac{1}{x}>\frac{1}{2}

    Then a little known rule says that if   \frac{a}{b}>\frac{c}{d} then   \frac{b}{a}<\frac{d}{c}
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  9. #9
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    Re: Solving Rational Inequalities

    Okay, I get it. Thank you
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  10. #10
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    Re: Solving Rational Inequalities

    Quote Originally Posted by Dragon08 View Post
    Solve this inequality: 5/6x+2/3x>3/4.
    So I simplified the left side and got 3/2x, then moved the equation to one side and got 3/2x-3/4>0. I got x>1/2, but the answer is wrong.
    Can somebody help me?

    Thanks in advance.
    A large part of your problem is that what you give as the question itself is ambiguous- use parentheses!

    If the problem was (5/6)x+(2/3)x>3/4, then x> 1/2 is exactly right. However, it appears that your problem is really 5/(6x)+ 2/(3x)> 3/4. If that is what the inequality is, then, as SammyS said, you arrive at 1/x> 1/2 so that 0< x< 2. (If 1/x> 1/2 then x must be positive.)
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