BECE Mathematics 2020 Paper

Concept:To solve a linear equation containing a fraction, first eliminate the denominator, then collect like terms and isolate the variable.Solution:Start with the given equation:$$\frac{w}{3} = 3(w-1) - 1$$Expand the bracket using the distributive property:$$3(w-1) = 3w - 3$$Substitute this back into the equation:$$\frac{w}{3} = 3w - 3 - 1$$Simplify the right-hand side:$$\frac{w}{3} = 3w - 4$$Multiply both sides by $3$ to remove the fraction:$$3 \times \frac{w}{3} = 3(3w - 4)$$This simplifies to:$$w = 9w - 12$$Subtract $9w$ from both sides to bring the variable terms together:$$w - 9w = -12$$$$-8w = -12$$Divide both sides by $-8$:$$\frac{-8w}{-8} = \frac{-12}{-8}$$$$w = \frac{12}{8}$$Simplify the fraction by dividing the numerator and denominator by their HCF, which is $4$:$$w = \frac{12 \div 4}{8 \div 4} = \frac{3}{2}$$Answer:Option A ($\frac{3}{2}$)