If \(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is
A
x > \(\frac{1}{3}\)
B
x < \(\frac{1}{3}\)
C
x < \(\frac{1}{4}\)
D
x < \(\frac{9}{16}\)
E
x > \(\frac{9}{16}\)
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
\(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 4^{\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 2 > \frac{1}{4} - x\)
= \(3x + x > \frac{1}{4} + 2 \implies 4x > \frac{9}{4}\)
\(x > \frac{9}{16}\)
Source: Myschool Past Questions Archive (Record #32703)