JEE Main & Advanced Mathematics Linear Programming Question Bank Mock Test - Linear Inequalities

  • question_answer
    The set of values of x which satisfy the inequations\[5x+2<3x+8\]and \[\frac{x+2}{x-1}<4\]is

    A) \[(-\infty ,\,1)\]  

    B) (2, 3)

    C) \[(-\infty ,\,3)\]  

    D) \[(-\infty ,\,1)\cup (2,3)\]

    Correct Answer: D

    Solution :

    [d] \[5x+2<3x+8\] \[\Rightarrow x<3\]                                 (1) And \[\left| \frac{{{x}^{2}}+1}{x} \right|>2\] \[\Rightarrow \frac{x-2}{x-1}>0\] \[\Rightarrow x<1\]or \[x>2\]                   (2) From (1) and (2), we get \[x\in (-\infty ,1)\cup (2,3)\].


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