BECE Mathematics 2016 Paper

Concept:To solve a linear inequality with a fraction, multiply both sides by the denominator to remove the fraction, then isolate $x$.Remember: multiplying or dividing an inequality by a negative number reverses the inequality sign.Explanation:Start with the given inequality:$$2x + 10 \ge \frac{7}{2}x - 5$$Multiply every term on both sides by $2$ to eliminate the fraction:$$2(2x + 10) \ge 2\left(\frac{7}{2}x - 5\right)$$This simplifies to:$$4x + 20 \ge 7x - 10$$Bring the variable terms to one side and constants to the other side:$$4x - 7x \ge -10 - 20$$$$-3x \ge -30$$Divide both sides by $-3$. Since we divide by a negative number, flip the inequality sign:$$\frac{-3x}{-3} \le \frac{-30}{-3}$$$$x \le 10$$Thus, the solution set is all values of $x$ that are less than or equal to $10$.Answer:$x \le 10$So, the correct option is B.