WAEC Mathematics 2012 Paper

Concept:The problem is a linear inequality in one variable. Clear the fractions first, then solve for $m$ while remembering to reverse the inequality sign when dividing by a negative number.Explanation:Start with the given inequality:$$\frac{-m}{2} - \frac{5}{4} \ge \frac{5m}{12} - \frac{7}{6}$$The LCM of the denominators $2$, $4$, $12$, and $6$ is $12$.Multiply every term by $12$:$$12\left(\frac{-m}{2}\right) - 12\left(\frac{5}{4}\right) \ge 12\left(\frac{5m}{12}\right) - 12\left(\frac{7}{6}\right)$$Simplify each term:$$-6m - 15 \ge 5m - 14$$Collect the $m$-terms on the left and constants on the right:$$-6m - 5m \ge -14 + 15$$Combine like terms:$$-11m \ge 1$$Divide both sides by $-11$. Since we divide by a negative number, the inequality sign reverses:$$m \le -\frac{1}{11}$$Answer:$\boxed{m \le -\frac{1}{11}}$Hence, the correct option is C. $m \le -\frac{1}{11}$.