Solve the inequality |5x-3| < 2|3x – 7|.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. B1 State or imply non-modular inequality (5x-3)² < 2² (3x – 7)², or corresponding quadratic equation, or pair of linear equations (5x – 3) = ±2(3x-7) [11x²-138x+187 > 0.]
2. M1 Solve a 3-term quadratic, or solve two linear equations for x [If no working is shown, the M1 is implied by the correct roots for an incorrect quadratic.]
3. A1 Obtain critical values x = 17/11 and x = 11 [Accept 1.55 or better.]
4. A1 Strict inequality required. In set notation, allow notation for open sets but not for closed sets e.g. accept (-∞, 17/11) ∪ (11, ∞) or (-∞, 17/11[ ∪ ]11, ∞) but not (-∞, 17/11] ∪ [11, ∞). Allow 'or' but not 'and'. Accept . Final A0 for 17/11 > x > 11. Exact values expected but ISW if exact inequalities seen followed by decimal approx.
5. Alternative Method for Question 1:
6. B1 Obtain critical value x = 11 from a graphical method, or by inspection, or by solving a linear equation or an inequality
7. B2 Obtain critical value x = 17/11 similarly [Accept decimal value.]
8. B1 Strict inequality required. See notes above.