Correct Answer: Option A

Explanation

12x² < x + 1

12 - x - 1 < 0

12x² - 4x + 3x - 1 < 0

4x(3x - 1) + (3x - 1) < 0

Case 1 (+, -)

4x + 1 > 0, 3x - 1 < 0

x > -\(\frac{1}{4}\)x < \(\frac{1}{3}\)

Case 2 (-, +) 4x + 1 < 0, 3x - 1 > 0

-\(\frac{1}{4}\) < x < - \(\frac{1}{3}\)

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