JAMB Mathematics 2014 Paper

Concept:To solve a linear inequality, first clear fractions by multiplying through by the least common multiple, then isolate $x$ and reverse the inequality sign when dividing by a negative number.Explanation:Multiply both sides by $12$, the L.C.M. of the denominators $2$, $4$, $6$, and $12$:$$12\left(\frac{x}{2}+\frac{3}{4}\right) \leq 12\left(\frac{5x}{6}-\frac{7}{12}\right)$$Simplify each term:$$6x + 9 \leq 10x - 7$$Bring like terms together:$$6x - 10x \leq -7 - 9$$$$-4x \leq -16$$Divide both sides by $-4$. Since we are dividing by a negative number, reverse the inequality sign:$$x \geq 4$$Answer:$x \geq 4$, so the correct option is A.