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 \(\geq - \frac{1}{11}\)

Correct answer is C

\(\frac{-m}{2} - \frac{5}{4} \geq \frac{5m}{12} - \frac{7}{6}\)

= \(\frac{-2m - 5}{4} \geq \frac{5m - 14}{12}\)

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 \(\leq \frac{-1}{11}\)