BECE Mathematics 2014 Paper

Concept:To solve a linear inequality, eliminate the fraction by multiplying both sides by the denominator and then isolate $x$.Remember: when dividing or multiplying an inequality by a negative number, the inequality sign reverses.Explanation:Start with the given inequality:$$2x+10 \geq \frac{7x}{2}-5$$Multiply both sides by $2$ to remove the fraction:$$2(2x+10) \geq 2\left(\frac{7x}{2}-5\right)$$$$4x+20 \geq 7x-10$$Bring the $x$ terms together and the constant terms together:$$4x-7x \geq -10-20$$$$-3x \geq -30$$Divide both sides by $-3$. Since we are dividing by a negative number, flip the inequality sign:$$x \leq \frac{-30}{-3}$$$$x \leq 10$$Answer:$$x \leq 10$$So, the correct option is A. $x \leq 10$.