WAEC - Further Mathematics (2024 - No. 21)

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 \(\geq\) \(\frac{1}{2}\)

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)