Find the set of values of x satisfying the inequality | 2x+1 – 2| < 0.5, giving your answer to 3 significant figures.

Mark scheme

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

1. [B1] State or imply non-modular inequality -0.5 < 2x+1 – 2 < 0.5, can be in two separate statements, or (2x+1 - 2)² < 0.5², or corresponding pair of linear equations 0.5 = 2x+1 – 2 and – 0.5 = 2x+1 – 2 or quadratic equation (2x+1 − 2)² = 0.5². -0.25 < 2x - 1 < 0.25, can be in two separate statements, or (2x - 1)² < 0.25² or corresponding pair of linear equations 0.25 = 2x – 1 and -0.25 = 2x – 1 or quadratic equation (2x - 1)² = 0.25². Incorrect inequality mark recoverable by correct final answer or x < 0.32 and x > -0.42.
2. [M1] Use correct method for solving an equation or inequality of the form 2x+1 = a or 2x = b where a, b > 0. Reach (x + 1)ln2 = lna or equivalent, do not need to reach x = ...
3. [A1] Obtain critical values x = 0.322 and -0.415 or awrt x = 0.32 and -0.42 or exact equivalents. e.g. (ln 2.5 / ln 2) – 1 and (ln 1.5 / ln 2) – 1.
4. [A1] State final answer -0.415 < x < 0.322 or (–0.415, 0.322). Need 3 significant figures. Need combined result, not x < 0.32 and x > -0.42. Must be strict inequalities. No working, 0/4.