NECO 2023 · Paper 1 · Q16

The difference between a non-negative number $x$ and 5 is twice the number or more. Find the range of values of the number.

Worked solution (try it first)

For $0 \le x \le 5$ the difference between $x$ and 5 is $5 - x$ , so the condition is $5 - x \ge 2x$ .
Add $x$ to both sides: $5 \ge 3x$ , so $x \le \frac53$ .
For $x > 5$ the difference is $x - 5$ , and $x - 5 \ge 2x$ would need $x \le -5$ , which a non-negative number can't be.
With $x \ge 0$ as well, the range is $0 \le x \le \frac53$ , option D.