Solve the inequality 2 – 5x > 2|x-3|.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. Make a recognisable sketch graph of y = 2|x-3| and the line y = 2-5x
2. Find x-coordinate of intersection with y = 2 – 5x
3. Obtain x = 4/3
4. State final answer x < -4/3
5. State or imply non-modular inequality/equality (2 - 5x)² >, >, =, 22(x – 3)2, or corresponding quadratic equation, or pair of linear equations (2 – 5x) >, >, =, ± 2(x − 3)
6. Make reasonable attempt at solving a 3-term quadratic, or solve one linear equation, or linear inequality for x
7. Obtain critical value x = 4/3
8. State final answer x < -4/3