JAMB Mathematics 2010 Paper

Concept:Solving a linear inequality by first removing fractions using the least common multiple (LCM) of the denominators.Explanation:Start with the inequality:$\frac{1}{2}x + \frac{1}{4} > \frac{1}{3}x + \frac{1}{2}$The denominators are $2$, $3$ and $4$, so the LCM is $12$.Multiply each term on both sides by $12$:$12 \times \frac{1}{2}x + 12 \times \frac{1}{4} > 12 \times \frac{1}{3}x + 12 \times \frac{1}{2}$Simplify each term:$6x + 3 > 4x + 6$Subtract $4x$ from both sides:$2x + 3 > 6$Subtract $3$ from both sides:$2x > 3$Divide both sides by $2$:$x > \frac{3}{2}$Answer:$x > \frac{3}{2}$, which is option B.