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

  • question_answer
    The set of real values of x satisfying \[\left| x-1 \right|\le 3\] and \[\left| x-1 \right|\ge 1\] is

    A) \[[2,4]\]

    B) \[(-\infty ,2]\cup [4,+\infty )\]

    C) \[[-2,0]\cup [2,4]\]

    D) None of these

    Correct Answer: C

    Solution :

    [c] \[\left| x-1 \right|\le 3\Rightarrow -3\le x-1\le 3\Rightarrow -2\le x\le 4\] and \[\left| x-1 \right|\ge 1\Rightarrow x-1\le -1\,\,or\,\,x-1\ge 1\] \[\Rightarrow x\le 0\,\,or\,\,x\ge 2\] Taking the common values of x, we get \[x\in [-2,0]\cup [2,4]\]


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