BECE Mathematics 2010 Paper

Concept:Solving a linear inequality requires simplifying and reversing the inequality sign when multiplying or dividing by a negative number.Explanation:Start with the given inequality:$$7x - (10x + 3) \ge -9$$Distribute the negative sign inside the bracket:$$7x - 10x - 3 \ge -9$$Combine like terms:$$-3x - 3 \ge -9$$Add $3$ to both sides to isolate the variable term:$$-3x \ge -9 + 3$$$$-3x \ge -6$$Now divide both sides by $-3$. Since we divide by a negative number, the inequality sign reverses: $\ge$ becomes $\le$.$$x \le \frac{-6}{-3}$$$$x \le 2$$Answer:$x \le 2$, which is Option D.