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

  • question_answer
    Solution set of the inequality \[6\le -3(2x-5)<12\]is

    A) \[(0,\,3/2)\]       

    B) \[\left( 1/2,\,3/2 \right]\]

    C) \[\left[ 1/2,\,3/2 \right)\]  

    D) \[\left[ 0,\,1/2 \right)\]

    Correct Answer: B

    Solution :

    [b] \[6\le -3(2x-5)<12\] \[\Rightarrow 2\le -(2x-5)<4\] \[\Rightarrow -2\ge 2x-5>-4\] \[\Rightarrow 5-2\ge 2x>5-4\] \[\Rightarrow 3\ge 2x>1\] \[\Rightarrow 3/2\ge x>1/2\] Thus, the solution set for the given inequality is (1/2, 3/2].


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