Solve the inequality |x-3| < 3x −4.

Mark scheme

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

1. [B1] State or imply non-modular inequality (x - 3)² < (3x-4)² , or corresponding equation
2. [M1] Make reasonable attempt at solving a three term quadratic
3. [A1] Obtain critical value x = 7/4
4. [A1] State final answer x > 7/4 only
5. [B1] State the relevant critical inequality 3-x < 3x-4, or corresponding equation
6. [M1] Solve for x
7. [A1] Obtain critical value x = 7/4
8. [A1] State final answer x > 7/4 only
9. [B1] Make recognizable sketches of y = |x-3| and y = 3x-4 on a single diagram
10. [M1] Find x-coordinate of the intersection
11. [A1] Obtain x = 7/4
12. [A1] State final answer x > 7/4 only