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JEE Main & Advanced Mathematics Equations and Inequalities Question Bank Self Evaluation Test - Linear Inequalities

  • question_answer
    If x satisfies the inequalities \[x+7<2x+3\] and \[2x+4<5x+3,\] then x lies in the interval

    A) \[(-\infty ,3)\]

    B) \[(1,3)\]

    C) \[(4,\infty )\]

    D)        \[(-\infty ,-1)\]

    Correct Answer: C

    Solution :

    [c] \[x+7<2x+3\]           \[2x+4<5x+3\] \[\left. \Rightarrow 4<x\,\,\,\,\,\,\,\,\, \right|\,\,\,\,\,\,\,\,\,\,1<3x\Rightarrow x>\frac{1}{3}\] so, \[x>\frac{1}{3}\,\,and\,\,x>4\,\,\,\,\therefore \] x lies in \[(4,\infty )\].


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