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 > \(\frac{9}{16}\)
Vysvětlení
\(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 4^{\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 2 > \frac{1}{4} - x\)
= \(3x + x > \frac{1}{4} + 2 \implies 4x > \frac{9}{4}\)
\(x > \frac{9}{16}\)