JAMB Mathematics 2020 Paper

Concept:For a positive real number $x$, multiplying every term by a positive number preserves the direction of the inequality.Explanation:Start with the inequality: $\frac{1}{3x}+\frac{1}{2}>\frac{1}{4x}$.Since $x>0$, multiply both sides by $12x$.$12x \times \frac{1}{3x} = 4$$12x \times \frac{1}{2} = 6x$$12x \times \frac{1}{4x} = 3$The inequality becomes $4+6x>3$.Subtract $4$ from both sides: $6x>-1$.Divide both sides by $6$: $x>-\frac{1}{6}$.But the condition in the question already states $x>0$.Combining $x>-\frac{1}{6}$ with $x>0$ gives $x>0$.Hence, every positive real number satisfies the inequality.Answer:$x>0$