WAEC 2019 · Paper 2 · Q1

(a)
Solve the inequality $\dfrac{1 + 4x}{2} - \dfrac{5 + 2x}{7} < x - 2$ .
Show the answer
$x < -2\frac12$
(b)
If $x : y = 3 : 5$ , find the value of $\dfrac{2x^2 - y^2}{y^2 - x^2}$ .

Worked solution (try it first)

(a)

Multiply every term by 14, the LCM of 2 and 7: $7(1 + 4x) - 2(5 + 2x) < 14(x - 2)$ .
Expand: $7 + 28x - 10 - 4x < 14x - 28$ .
So $24x - 3 < 14x - 28$ .
Collect terms: $10x < -25$ .
Divide by 10: $x < -2\frac12$ .

(b)

$x : y = 3 : 5$ means $x = 3k$ and $y = 5k$ for some number $k$ .
Substitute: $\frac{2(3k)^2 - (5k)^2}{(5k)^2 - (3k)^2} = \frac{18k^2 - 25k^2}{25k^2 - 9k^2}$
$= \frac{-7k^2}{16k^2}$
$= -\frac{7}{16}$ .

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