JAMB Mathematics 2012 Paper

Concept:Solve the linear inequality by isolating $y$, and reverse the inequality sign when multiplying or dividing by a negative number.Explanation:Start with:$$\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}$$Collect like terms by subtracting $\frac{1}{2}y$ and $\frac{1}{5}$ from both sides:$$\frac{1}{5}y - \frac{1}{2}y < \frac{2}{5} - \frac{1}{5}$$Combine the fractions:$$\frac{2y - 5y}{10} < \frac{1}{5}$$This simplifies to:$$-\frac{3y}{10} < \frac{1}{5}$$Multiply both sides by $10$:$$-3y < 2$$Now divide both sides by $-3$, remembering to reverse the inequality sign:$$y > -\frac{2}{3}$$Answer:$y > -\frac{2}{3}$, which matches option C.