BECE Mathematics 2018 Paper

Concept:Solving a linear inequality by eliminating fractions and reversing the inequality sign when dividing by a negative number.Explanation:Start with the given inequality: $\frac{1}{2}(3x-1)+1 \le 7+2x$Multiply every term by $2$ to remove the fraction: $2 \times \frac{1}{2}(3x-1)+2 \times 1 \le 2 \times 7+2 \times 2x$This simplifies to: $3x-1+2 \le 14+4x$Combine like terms on the left side: $3x+1 \le 14+4x$Bring the variable terms to one side and constants to the other: $3x-4x \le 14-1$Simplify: $-x \le 13$Divide both sides by $-1$. Since we divide by a negative number, the inequality sign reverses: $\frac{-x}{-1} \ge \frac{13}{-1}$Thus: $x \ge -13$Answer:$x \ge -13$, which is option C.