JAMB - Mathematics (1978 - No. 19)

If \(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is

x > \(\frac{1}{3}\)

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

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

x < \(\frac{9}{16}\)

x > \(\frac{9}{16}\)

\(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x\)

= \(3x - 4^{\frac{1}{2}} > \frac{1}{4} - x\)

= \(3x - 2 > \frac{1}{4} - x\)

= \(3x + x > \frac{1}{4} + 2 \implies 4x > \frac{9}{4}\)

\(x > \frac{9}{16}\)