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

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. EITHER: State or imply non-modular inequality (2x + 1)² < (3(x−2))², or corresponding quadratic equation, or pair of linear equations (2x + 1) = ±3(x – 2) (B1
2. Make reasonable solution attempt at a 3-term quadratic e.g. 5x² – 40x + 35 = 0 or solve two linear equations for x M1
3. Obtain critical values x = 1 and x = 7 A1
4. State final answer x < 1 and x > 7 A1)
5. OR: Obtain critical value x = 7 from a graphical method, or by inspection, or by solving a linear equation or inequality (B1
6. Obtain critical value x = 1 similarly B2
7. State final answer x < 1 and x > 7 B1)