Standard +0.3 This is a straightforward modulus inequality requiring students to consider two cases (x ≥ 2 and x < 2) and solve linear inequalities in each case, then combine the solutions. It's slightly above average difficulty as it requires systematic case analysis and careful attention to the domain restrictions, but the algebraic manipulation is routine and the concept is a standard P3 topic.
EITHER State or imply non-modular inequality \((x-2)^2 < (3-2x)^2\), or corresponding equation
B1
Expand and make a reasonable solution attempt at a 2- or 3-term quadratic, or equivalent
OR State the relevant linear equation for a critical value, i.e. \(2 - x = 3 - 2x\), or equivalent
B1
Obtain critical value \(x = 1\)
OR Obtain the critical value \(x = 1\) from a graphical method, or by inspection, or by solving a linear inequality
B2
State answer \(x < 1\)
**EITHER** State or imply non-modular inequality $(x-2)^2 < (3-2x)^2$, or corresponding equation | B1 | Expand and make a reasonable solution attempt at a 2- or 3-term quadratic, or equivalent | M1 | Obtain critical value $x = 1$ | A1 | State answer $x < 1$ only | A1 |
**OR** State the relevant linear equation for a critical value, i.e. $2 - x = 3 - 2x$, or equivalent | B1 | Obtain critical value $x = 1$ | B1 | State answer $x < 1$ | B1 | State or imply by omission that no other answer exists | B1 |
**OR** Obtain the critical value $x = 1$ from a graphical method, or by inspection, or by solving a linear inequality | B2 | State answer $x < 1$ | B1 | State or imply by omission that no other answer exists | B1 | **[4]**