JAMB 1997 · UME · Q17

Let $f(x) = 2x + 4$ and $g(x) = 6x + 7$ , where $g(x) > 0$ . Solve the inequality $\dfrac{f(x)}{g(x)} < 1$ .

Worked solution (try it first)

$g(x) > 0$ , so you can multiply both sides by $g(x)$ without reversing the sign: $2x + 4 < 6x + 7$ .
Subtract $2x$ and 7 from both sides: $-3 < 4x$ .
Divide by 4: $x > -\frac34$ , option C.