Standard +0.3 This is a standard modulus inequality requiring consideration of critical points (x=4 and x=8) and testing regions, which is a routine technique taught in P2. While it requires systematic case analysis across three intervals, the algebraic manipulation within each case is straightforward, making it slightly easier than average but not trivial.
State or imply non-modular inequality \((x - 8)^2 > (2x - 4)^2\), or corresponding equation or pair of linear equations
M1
Make reasonable solution attempt at a quadratic, or solve two linear equations
M1
Obtain critical values 4 and -4
A1
State correct answer \(-4 < x < 4\)
A1
[4]
Or
Answer
Marks
Guidance
Obtain one critical value, e.g. \(x = 4\), by solving a linear equation (or inequality) or from a graphical method or by inspection
B1
Obtain the other critical value similarly
B2
State correct answer \(-4 < x < 4\)
B1
[4]
**Either**
State or imply non-modular inequality $(x - 8)^2 > (2x - 4)^2$, or corresponding equation or pair of linear equations | M1 |
Make reasonable solution attempt at a quadratic, or solve two linear equations | M1 |
Obtain critical values 4 and -4 | A1 |
State correct answer $-4 < x < 4$ | A1 | [4]
**Or**
Obtain one critical value, e.g. $x = 4$, by solving a linear equation (or inequality) or from a graphical method or by inspection | B1 |
Obtain the other critical value similarly | B2 |
State correct answer $-4 < x < 4$ | B1 | [4]