JAMB Mathematics 2019 Paper

Concept:Solve a linear inequality involving fractions by clearing denominators and isolating $x$.Explanation:Start with the inequality:$$\frac{2+2x}{3} - 2 \geq \frac{4x-6}{5}$$Rewrite the left side with a common denominator of $3$:$$\frac{2+2x-6}{3} \geq \frac{4x-6}{5}$$Simplify the numerator on the left:$$\frac{2x-4}{3} \geq \frac{4x-6}{5}$$Cross-multiply. Both denominators are positive, so the inequality direction stays the same:$$5(2x-4) \geq 3(4x-6)$$Expand both sides:$$10x - 20 \geq 12x - 18$$Collect the $x$-terms on one side and the constants on the other:$$10x - 12x \geq -18 + 20$$$$-2x \geq 2$$Divide both sides by $-2$. Remember to reverse the inequality sign when dividing by a negative number:$$x \leq -1$$Answer:$$x \leq -1$$This matches option C.