JAMB Mathematics 2018 Paper

Concept:Solving a linear inequality by first removing fractions, then isolating the variable and reversing the inequality sign when dividing by a negative number.Explanation:Start with the given inequality:$$\frac{x+2}{4} - \frac{2x-3}{3} < 4$$Multiply every term by the common denominator $12$:$$3(x+2) - 4(2x-3) < 48$$Expand the brackets:$$3x + 6 - 8x + 12 < 48$$Simplify the left-hand side:$$18 - 5x < 48$$Subtract $18$ from both sides:$$-5x < 30$$Divide both sides by $-5$ and reverse the inequality sign:$$x > -6$$Therefore, the values of $x$ that satisfy the inequality are all numbers greater than $-6$.Answer:$$x > -6$$This corresponds to option B.