JAMB 1997 · UME · Q18

Find the range of values of $x$ which satisfies the inequality $12x^2 < x + 1$ .

Worked solution (try it first)

Bring everything to one side: $12x^2 - x - 1 < 0$ .
Factorise: $(4x + 1)(3x - 1) < 0$ , so the roots are $x = -\frac14$ and $x = \frac13$ .
"Less than 0" means between the roots: $-\frac14 < x < \frac13$ , option A.