Solve the inequality: \(\frac{-m}{2} - \frac{5}{4} \geq \frac{5m}{12} - \frac{7}{6}\)
A
m \(\leq \frac{5}{4}\)
B
m \(\geq \frac{5}{4}\)
C
m \(\leq - \frac{1}{11}\)
D
m \(\geq - \frac{1}{11}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{-m}{2} - \frac{5}{4} \geq \frac{5m}{12} - \frac{7}{6}\)
= \(\frac{-2m - 5}{4} \geq \frac{5m - 14}{12}\)
12(-2m - 5) \(\geq\) 4(5m - 14)
-24m - 60 \(\geq\) 20m - 56
-24m - 20m \(\geq\) -56 + 60
44m \(\geq\) 4
m \(\leq \frac{4}{-44}\)
m \(\leq \frac{-1}{11}\)
Source: Myschool Past Questions Archive (Record #36760)