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If the inequality (2m + x)/3 ≤ (4mx - 1)/2 has solution set x ≥ 3/4, what is the value of the parameter m?

1. 7/10
2. 9/10
3. 9/11
4. None of these

Correct answer: 9/10

Solution

(2m+x)/3 <= (4mx-1)/2 -> 4m+2x <= 12mx-3 -> x(12m-2) >= 4m+3 -> x >= (4m+3)/(12m-2). Setting (4m+3)/(12m-2) = 3/4 gives 16m+12 = 36m-6, so 20m = 18 and m = 9/10.

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