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Math Help - Linear Inequality

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    Senior Member sakonpure6's Avatar
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    Linear Inequality

    3/(x-4) < 5 - Wolfram|Alpha

    For the inequality on wolfram-alpha, how do you get the algebraic the solution x < 4 ? I only get x > 23/5 when solving algebraically.
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    Re: Linear Inequality

    Quote Originally Posted by sakonpure6 View Post
    3/(x-4) < 5 - Wolfram|Alpha

    For the inequality on wolfram-alpha, how do you get the algebraic the solution x < 4 ? I only get x > 23/5 when solving algebraically.
    Write it as 0<5-\frac{3}{x-4}=\frac{5x-23}{x-4}.

    Consider the three regions: \left( { - \infty ,4} \right),\quad \left( {4,4.6} \right),\quad \left( {4.6,\infty } \right)

    \frac{5x-23}{x-4}. is positive on the first and third region.
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    Senior Member sakonpure6's Avatar
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    Re: Linear Inequality

    Oh okay, much appreciated!
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    Re: Linear Inequality

    Quote Originally Posted by sakonpure6 View Post
    3/(x-4) < 5 - Wolfram|Alpha

    For the inequality on wolfram-alpha, how do you get the algebraic the solution x < 4 ? I only get x > 23/5 when solving algebraically.
    I believe you have two cases:
    1) x-4 >0
    2) x-4 <0

    You've only worked out case 1.

    For case 2, you end up with x<\frac{23}{5}. This is a condition and is satisfied whenever x-4<0.
    Hence, in the case where x-4<0, the inequality is satisfied by all such x. That's where the x<4 comes from.
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