(a) Solve the inequality: (frac{1 + 4x}{2}) -(frac{5 + 2x}{7}) < x -2
(b) If x: y = 3: 5, find the value of (frac{2x^2 – y^2}{y^2 – x^2})
Explanation
(a) majority of the candidates multiplied through by the L.C.M which is 14 to arrive at 7(1+4x) – 2(5+2x) < 14(x – 2) and when simplified yielded 10x < -25 x -2(frac{1}{2})
(b) it was expected that they express x = (frac{3y}{5}) or y = (frac{5x}{3}) and thereafter, substitute into the given expression to have (frac{2x^2 – y^2}{y^2 – x^2} = frac{2x^2 – (frac{5x}{3})^2}{(frac{5x}{3})^2 – x^2} = frac{x^(2 – frac{25}{9})}{x^2(frac{25}{9} – 1)} = frac{-7}{16})