Standard +0.3 This is a straightforward modulus inequality requiring consideration of critical points (x = -3 and x = 0) and testing regions, which is a standard technique taught in P2. While it requires systematic case analysis, it's a routine application of the method with no conceptual surprises, making it slightly easier than average.
Obtain a non-modular inequality from \((x + 3)^2 > (2x)^2\), or corresponding equation, or pair of linear equations \((x + 3) = \pm 2x\)
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(x = -1\) and \(x = 3\)
A1
State answer \(-1 < x < 3\)
A1
OR:
Answer
Marks
Obtain critical value \(x = 3\) from a graphical method, or by inspection, or by solving a linear inequality or linear equation
B1
Obtain the critical value \(x = -1\) similarly
B2
State answer \(-1 < x < 3\)
B1
Total: [4]
**EITHER:**
| Obtain a non-modular inequality from $(x + 3)^2 > (2x)^2$, or corresponding equation, or pair of linear equations $(x + 3) = \pm 2x$ | M1 |
| Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
| Obtain critical values $x = -1$ and $x = 3$ | A1 |
| State answer $-1 < x < 3$ | A1 |
**OR:**
| Obtain critical value $x = 3$ from a graphical method, or by inspection, or by solving a linear inequality or linear equation | B1 |
| Obtain the critical value $x = -1$ similarly | B2 |
| State answer $-1 < x < 3$ | B1 |
**Total: [4]**
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