Solve the inequality | 3x+2|<3|2x-1|.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. State or imply non-modular inequality (3x+2)² <3²(2x−1)², or pair of linear equations (3x + 2) = + 3(2x – 1)
2. Make reasonable attempt at solving a 3-term quadratic, or solve two linear equations for x
3. Obtain critical values x = 1/9 and x = 5/3
4. State final answer x < 1/9, x > 5/3 only
5. Obtain critical value x = 5/3 from a graphical method, or by inspection, or by solving a linear equation or an inequality
6. Obtain critical value x = 1/9 similarly
7. State final answer x < 1/9, x > 5/3 only