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Thread: Solving ineqality problem

  1. August 7th 2011, 09:58 PM #1
    haftakhan
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    Question Solving ineqality problem

    given that (4x/5)-(1/10)<=x-(2/5), state the smallest value of x when

    1)x is an integer

    2)x is prime number

    3)x is a rational number

    please guide me on how should i solve these ?
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  2. August 7th 2011, 10:01 PM #2
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    Re: Solving ineqality problem

    Start by solving the inequality...
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  3. August 7th 2011, 10:06 PM #3
    haftakhan
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    Re: Solving ineqality problem

    answer comes as 4.5<=x

    but what should i do then ?
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  4. August 7th 2011, 10:26 PM #4
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    Re: Solving ineqality problem

    Quote Originally Posted by haftakhan View Post
    answer comes as 4.5<=x

    but what should i do then ?
    I don't get \displaystyle 4.5 \leq x...


    \displaystyle \begin{align*} \frac{4x}{5} - \frac{1}{10} &\leq x - \frac{2}{5} \\ \frac{4x}{5} + \frac{3}{10} &\leq x \\ \frac{3}{10} &\leq \frac{x}{5} \\ \frac{3}{2} &\leq x \end{align*}

    What is the smallest integer which satisfies this inequality? What is the smallest prime number? What is the smallest rational number?
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  5. August 11th 2011, 09:56 PM #5
    haftakhan
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    Re: Solving ineqality problem

    How u get 3/10 after solving (-1/10)+(2/5) ?
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  6. August 11th 2011, 10:27 PM #6
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    Re: Solving ineqality problem

    \displaystyle -\frac{1}{10} + \frac{2}{5} = -\frac{1}{10} + \frac{4}{10} = \frac{3}{10}
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  7. August 12th 2011, 03:09 PM #7
    haftakhan
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    Re: Solving ineqality problem

    Integer is 1

    Prime number will be 1 as well

    Rational number ???
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  8. August 12th 2011, 03:18 PM #8
    Plato
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    Re: Solving ineqality problem

    Quote Originally Posted by haftakhan View Post
    Prime number will be 1 as well
    The number 1 is not prime.
    If you do not know that, you should not attempt this question.
    Moreover, anyone asked to do this question surely knows what a rational number is.
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  9. August 12th 2011, 03:20 PM #9
    e^(i*pi)
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    Re: Solving ineqality problem

    Quote Originally Posted by haftakhan View Post
    Integer is 1

    Prime number will be 1 as well

    Rational number ???
    For that matter 1 is also smaller than 3/2 so it doesn't satisfy the inequality
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  10. August 12th 2011, 04:35 PM #10
    haftakhan
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    Re: Solving ineqality problem

    Sorry ,i thought x was lesser than 3/2

    integer and prime number should be 2
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  11. August 12th 2011, 06:08 PM #11
    HallsofIvy
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    Re: Solving ineqality problem

    Quote Originally Posted by haftakhan View Post
    Sorry ,i thought x was lesser than 3/2

    integer and prime number should be 2
    Okay, and your condition was that x\ge \frac{3}{2}. What is the smallest rational number satifying that?
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  12. August 12th 2011, 09:37 PM #12
    haftakhan
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    Re: Solving ineqality problem

    It would be 3/2
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  13. August 13th 2011, 04:37 AM #13
    e^(i*pi)
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    Re: Solving ineqality problem

    Quote Originally Posted by haftakhan View Post
    It would be 3/2
    Correct.
    Last edited by e^(i*pi); August 13th 2011 at 05:14 AM. Reason: OP answered the question already!
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  14. August 13th 2011, 04:49 AM #14
    HallsofIvy
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    Re: Solving ineqality problem

    Yes, e^ipi, he said that in post #10.
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