The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is
A
\(y > \frac{2}{3}\)
B
\(y < \frac{2}{3}\)
C
\(y > -\frac{2}{3}\)
D
\(y < -\frac{2}{3}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\)
Collect like terms
\(\frac{y}{5} - \frac{y}{2} < \frac{2}{5} - \frac{1}{5}\)
\(\frac{2y - 5y}{10} < \frac{2 - 1}{5}\)
\(\frac{-3y}{10} < \frac{1}{5}\)
\(y > \frac{-2}{3}\)
Source: Myschool Past Questions Archive (Record #27326)