2008 WAEC Mathematics Theory (a) Solve the inequality : \(\frac{2}{5}(x - 2) - \frac{1}{6}(x + 5) \leq 0\). (b)...

(a) Solve the inequality : \(\frac{2}{5}(x - 2) - \frac{1}{6}(x + 5) \leq 0\).

(b) Given that P = \(\frac{x^{2} - y^{2}}{x^{2} + xy}\),

(i) express P in its simplest form ; (ii) find the value of P if x = -4 and y = -6.

(a) \(\frac{2}{5}(x - 2) - \frac{1}{6}(x + 5) \leq 0\)

Multiplying through by the LCM of 5 and 6 (i.e 30)

\(12(x - 2) - 5(x + 5) \leq 0\)

\(12x - 24 - 5x - 25 \leq 0\)

\(7x - 49 \leq 0 \implies 7x \leq 49\)

\(x \leq 7\).

(b) (i) \(\frac{x^{2} - y^{2}}{x^{2} + xy}\)

P = \(\frac{(x - y)(x + y)}{x (x + y)}\)

P = \(\frac{x - y}{x}\)

(ii) When x = -4, y = -6

\(P = \frac{-4 - (-6)}{-4}\)

\(P = \frac{2}{-4}\)

\(P = - \frac{1}{2}\)

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