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

  • question_answer
    The solution set of \[\frac{2x-1}{3}\ge \left( \frac{3x-2}{4} \right)-\left( \frac{2-x}{5} \right)\] is\[(-\infty ,a]\]. The value of ?a? is

    A) 2

    B) 3

    C) 4

    D) 5

    Correct Answer: A

    Solution :

    [a] \[\frac{2x-1}{3}\ge \frac{15x-10-8+4x}{20}\] \[\Rightarrow \,\,\,\,\,\frac{2x-1}{3}\ge \frac{19x-18}{20}\] \[\Rightarrow 40x-20\ge 57x-54\Rightarrow -17x\ge -34\Rightarrow x\le 2\] \[\Rightarrow \,\,\,x\in (-\infty ,\,\,2]\]


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