1 Solve the inequality \(| 3 x - 5 | < 2 | x |\).
Show mark scheme
Show mark scheme source
Question 1: Either method:
Answer Marks
Guidance
Answer Marks
Guidance
State or imply non-modular inequality \((3x-5)^2 < 4x^2\) or corresponding equation or pair of linear equations B1 SC: Common error \((3x-5)^2 < 2x^2\)
Attempt solution of 3-term quadratic equation or solution of 2 linear equations M1 Obtain critical values 1 and 5 A1 Critical values \(\frac{15 \pm 5\sqrt{2}}{7}\) or 3.15, 1.13 allow B1
State correct answer \(1 < x < 5\) A1 \(\frac{15-5\sqrt{2}}{7} < x < \frac{15+5\sqrt{2}}{7}\) or \(1.13 < x < 3.15\) B1; Max 2/4; Allow M1 for \((7x \pm 5)(x \pm 5)\)
Or method:
Answer Marks
Guidance
Answer Marks
Guidance
Obtain \(x = 5\) by solving linear equation or inequality or from graphical method or inspection B1 Allow B1 for 5 seen, maybe in an inequality
Obtain \(x = 1\) similarly B2 Allow B2 for 1 seen, maybe in an inequality
State correct answer \(1 < x < 5\) B1 Total 4
Copy
**Question 1:**
**Either method:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply non-modular inequality $(3x-5)^2 < 4x^2$ or corresponding equation or pair of linear equations | **B1** | SC: Common error $(3x-5)^2 < 2x^2$ |
| Attempt solution of 3-term quadratic equation or solution of 2 linear equations | **M1** | |
| Obtain critical values 1 and 5 | **A1** | Critical values $\frac{15 \pm 5\sqrt{2}}{7}$ or 3.15, 1.13 allow B1 |
| State correct answer $1 < x < 5$ | **A1** | $\frac{15-5\sqrt{2}}{7} < x < \frac{15+5\sqrt{2}}{7}$ or $1.13 < x < 3.15$ B1; Max 2/4; Allow M1 for $(7x \pm 5)(x \pm 5)$ |
**Or method:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Obtain $x = 5$ by solving linear equation or inequality or from graphical method or inspection | **B1** | Allow B1 for 5 seen, maybe in an inequality |
| Obtain $x = 1$ similarly | **B2** | Allow B2 for 1 seen, maybe in an inequality |
| State correct answer $1 < x < 5$ | **B1** | |
| **Total** | **4** | |
Show LaTeX source
Copy
1 Solve the inequality $| 3 x - 5 | < 2 | x |$.\\
\hfill \mbox{\textit{CAIE P2 2018 Q1 [4]}}