Standard +0.8 This requires systematic case analysis of two modulus expressions with different critical points (x=4 and x=-1/3), solving multiple inequalities across three regions, and combining solutions. More demanding than routine single-modulus problems but follows standard technique for A-level.
EITHER: State or imply non-modular inequality \((x-4)^2 < (2(3x+1))^2\), or corresponding quadratic equation, or pair of linear equations \(x - 4 = \pm 2(3x+1)\)
(B1)
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for \(x\)
M1
Obtain critical values \(x = -\frac{6}{5}\) and \(x = \frac{2}{7}\)
A1
State final answer \(x < -\frac{6}{5}\), \(x > \frac{2}{7}\)
A1)
OR: Obtain critical value \(x = -\frac{6}{5}\) from graphical method, by inspection, or by solving a linear equation or inequality
(B1)
Obtain critical value \(x = \frac{2}{7}\) similarly
B2
State final answer \(x < -\frac{6}{5}\), \(x > \frac{2}{7}\)
B1)
Total: 4
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| **EITHER:** State or imply non-modular inequality $(x-4)^2 < (2(3x+1))^2$, or corresponding quadratic equation, or pair of linear equations $x - 4 = \pm 2(3x+1)$ | (B1) | |
| Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for $x$ | M1 | |
| Obtain critical values $x = -\frac{6}{5}$ and $x = \frac{2}{7}$ | A1 | |
| State final answer $x < -\frac{6}{5}$, $x > \frac{2}{7}$ | A1) | |
| **OR:** Obtain critical value $x = -\frac{6}{5}$ from graphical method, by inspection, or by solving a linear equation or inequality | (B1) | |
| Obtain critical value $x = \frac{2}{7}$ similarly | B2 | |
| State final answer $x < -\frac{6}{5}$, $x > \frac{2}{7}$ | B1) | |
**Total: 4**
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