WAEC Mathematics 2019 Paper

Concept:To solve a linear equation involving fractions, eliminate the denominators by multiplying every term by the least common multiple (LCM) of the denominators.Explanation:The given equation is: $$\frac{y+1}{2} - \frac{2y-1}{3} = 4$$ The denominators are $2$ and $3$, so the LCM is $6$. Multiply both sides of the equation by $6$ to remove the fractions: $$6 \times \frac{y+1}{2} - 6 \times \frac{2y-1}{3} = 6 \times 4$$ Simplifying each term gives: $$3(y+1) - 2(2y-1) = 24$$ Now expand the brackets inside the equation: $$3y + 3 - 4y + 2 = 24$$ Combine the like terms $3y$ and $-4y$, then $3$ and $2$: $$-y + 5 = 24$$ Subtract $5$ from both sides to isolate the $-y$ term: $$-y = 24 - 5$$ $$-y = 19$$ Finally, multiply both sides by $-1$ to get: $$y = -19$$Answer:$$y = -19$$ Hence, the correct option is B.