Solve the inequality |3x – a| > 2|x + 2a|, where a is a positive constant.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [B1] State or imply non-modular inequality (3x−a)² > 2² (x+2a)², or corresponding quadratic equation, or pair of linear equations or linear inequalities
2. [M1] Make reasonable attempt to solve a 3-term quadratic, or solve two linear equations for x in terms of a
3. [A1] Obtain critical values x = 5a and x = −3/5 a and no others
4. [A1] State final answer x > 5a, x < −3/5 a
5. Alternative method for Question 2
6. [B1] Obtain critical value x = 5a from a graphical method, or by solving a linear equation or linear inequality
7. [B2] Obtain critical value x = −3/5 a similarly
8. [B1] State final answer x > 5a, x < −3/5 a