Find the range of values of x for which 9x – 1 > 14x\(^2\)
-
\(\frac{1}{7}\) < x < \(\frac{1}{2}\)
- -\(\frac{1}{7}\) < x < \(\frac{1}{2}\)
- x \(\leq\) -\(\frac{1}{7}\) or x \(\geq\) \(\frac{1}{2}\)
- x \(\leq\) \(\frac{1}{7}\) or x \(\geq\) \(\frac{1}{2}\)
The correct answer is: 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)