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Find the range of values of x which satisfies the inequality 12x2

Find the range of values of x which satisfies the inequality 12x2

  • A.
    -(frac{1}{4})
  • B.
    (frac{1}{4})
  • C.
    -(frac{1}{3})
  • D.
    -(frac{1}{4})
Correct Answer: Option A
Explanation

12x2
12 – x – 1

12x2 – 4x + 3x – 1

4x(3x – 1) + (3x – 1)

Case 1 (+, -)
4x + 1 > 0, 3x – 1

x > -(frac{1}{4})x

Case 2 (-, +) 4x + 1 0
-(frac{1}{4})