Standard +0.3 This requires squaring both sides to eliminate moduli, expanding and simplifying a quadratic inequality, then factorising - a standard multi-step technique for AS/A2 level. While it involves several steps, the method is routine and commonly practiced in P2 courses, making it slightly above average difficulty but not requiring novel insight.
State or imply non-modulus inequality \((3x-7)^2 < (4x+5)^2\) or corresponding equation or pair of linear equations
B1
Attempt solution of 3-term quadratic equation/inequality or of two linear equations
M1
Obtain critical values \(-12\) and \(\dfrac{2}{7}\)
A1
May be seen in a number line.
State answer \(x < -12\), \(x > \dfrac{2}{7}\) or \((-\infty, -12) \cup \left(\dfrac{2}{7}, \infty\right)\) or \((-\infty, -12)\), \(\left(\dfrac{2}{7}, \infty\right)\)
A1
OE; \(-12 > x > \dfrac{2}{7}\) or similar would get A0. Mark the final answer.
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply non-modulus inequality $(3x-7)^2 < (4x+5)^2$ or corresponding equation or pair of linear equations | **B1** | |
| Attempt solution of 3-term quadratic equation/inequality or of two linear equations | **M1** | |
| Obtain critical values $-12$ and $\dfrac{2}{7}$ | **A1** | May be seen in a number line. |
| State answer $x < -12$, $x > \dfrac{2}{7}$ or $(-\infty, -12) \cup \left(\dfrac{2}{7}, \infty\right)$ or $(-\infty, -12)$, $\left(\dfrac{2}{7}, \infty\right)$ | **A1** | OE; $-12 > x > \dfrac{2}{7}$ or similar would get A0. Mark the final answer. |
| | **4** | |