Correct Answer: Option A

Explanation

9x - 1 > 14x\(^2\)

Rearrange the inequality

14x\(^2\) - 9x + 1 < 0 

14x\(^2\) - 7x - 2x + 1 < 0

7x(2x - 1) - 1(2x - 1) < 0

(7x - 1)(2x - 1) < 0

x < \(\frac{1}{7}\) or \(\frac{1}{2}\)

Final answer is \(\frac{1}{7}\) < x < \(\frac{1}{2}\) (after testing)

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