Standard +0.3 This is a standard modulus inequality requiring consideration of critical points (x = 0.5 and x = -4) and testing regions, but the algebraic manipulation is straightforward. Slightly above average difficulty as it requires systematic case analysis rather than just routine manipulation, but this is a well-practiced technique at A-level.
EITHER State or imply non-modular inequality \((2x-1)^2 < (x+4)^2\), or corresponding equation or pair of linear equations
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(-1\) and \(5\)
A1
State correct answer \(-1 < x < 5\)
A1
[4]
OR Obtain one critical value, e.g. \(x = 5\), 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 \(-1 < x < 5\)
B1
**EITHER** State or imply non-modular inequality $(2x-1)^2 < (x+4)^2$, or corresponding equation or pair of linear equations | M1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $-1$ and $5$ | A1 |
State correct answer $-1 < x < 5$ | A1 | [4]
**OR** Obtain one critical value, e.g. $x = 5$, 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 $-1 < x < 5$ | B1 |