Solve the inequality |3x – 5| < 2|x|.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. B1 State or imply non-modular inequality (3x-5)² <4x² or corresponding equation or pair of linear equations
2. M1 Attempt solution of 3-term quadratic equation or solution of 2 linear equations
3. A1 Obtain critical values 1 and 5
4. A1 State correct answer 1 <x<5
5. SC: Common error (3x-5)² <2x²
6. Critical values (15±5√2)/7 or 3.15, 1.13 allow B1
7. A1 (15-5√2)/7 <x< (15+5√2)/7 or 1.13 <x<3.15 B1
8. Max 2/4
9. Allow M1 for (7x+5)(x+5)
10. B1 Obtain x = 5 by solving linear equation or inequality or from graphical method or inspection
11. B2 Obtain x = 1 similarly
12. B1 State correct answer 1 <x<5
13. Allow B1 for 5 seen, maybe in an inequality
14. Allow B2 for 1 seen, maybe in an inequality