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

  • question_answer
    Solution set of the following inequalities is \[2(x-1)<x+5,3(x+2)>2-x\]

    A) \[(-1,\,7)\]         

    B) \[(1,\,7)\]

    C) \[(-1,\,\infty )\]  

    D) \[(-\infty ,\,7)\]

    Correct Answer: A

    Solution :

    [a] \[2(x-1)<x+5\] \[\Rightarrow 2x-2<x+5\] \[\Rightarrow 2x-x<5+2\] \[\Rightarrow x<7\]                                 (1) \[3(x+2)>2-x\] \[\Rightarrow 3x+6>2-x\] \[\Rightarrow 3x+x>2-6\] \[\Rightarrow 4x>-4\] \[\Rightarrow x>-1\]                             (2) For (1) and (2) it can be concluded that solution set for the given system of inequalities is (-1,7).


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