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

  • question_answer
    The solution set of the inequality \[37-(3x+5)\ge 9x-8(x-3)\] is

    A) \[(-\infty ,2)\]

    B) \[(-\infty ,-2)\]

    C) \[(-\infty ,2]\]

    D) \[(-\infty ,-2]\]  

    Correct Answer: C

    Solution :

    [c] We have, \[37-(3x+5)\ge 9x-8(x-3)\]\[(37-3x-5)\ge 9x-8x+24\] \[\Rightarrow 32-3x\ge x+24\] Transferring the term 24 to L.H.S. and the term \[(-3x)\] to R.H.S. \[32-24\ge x+3x\Rightarrow 8\ge 4x\Rightarrow 4x\le 8\] Dividing both sides by 4. \[\frac{4x}{4}\le \frac{8}{4}\Rightarrow x\le 2\] \[\therefore \] Solution set is \[(-\infty ,2].\]


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