Find the value of x satisfying \(\frac{x}{2}\) - \(\frac{1}{3}\) < \(\frac{2x}{5}\) + \(\frac{1}{6}\)
A
x < 5
B
x < 7\(\frac{1}{2}\)
C
x > 5
D
x > 7\(\frac{1}{2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{x}{2} - \frac{1}{3} < \frac{2x}{5} + \frac{1}{6}\)
\(\frac{x}{2} - \frac{2x}{5} < \frac{1}{6} + \frac{1}{3}\)
\(\frac{x}{10} < \frac{1}{2}\)
\(2x < 10 \implies x < 5\)
Source: Myschool Past Questions Archive (Record #32550)