NECO 2023 · Paper 1 · Q6

Solve the inequality $2x + \frac34 \le 5x - \frac23$ .

Worked solution (try it first)

Take $2x$ from both sides: $\frac34 \le 3x - \frac23$ .
Then add $\frac23$ to both sides: $\frac34 + \frac23 \le 3x$ .
Add the fractions over 12: $\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$ , so $\frac{17}{12} \le 3x$ .
Divide both sides by 3 (a positive number, so the sign stays): $\frac{17}{36} \le x$ .
So $x \ge \frac{17}{36}$ , option D.