2 Solve the inequality \(| x - 7 | > 4 x + 3\).
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Question 2:
Answer Marks
Guidance
Answer Mark
Guidance
Attempt solution of equation or inequality, where signs of \(x\) and \(4x\) are different M1
Obtain \(\frac{4}{5}\) A1
OE
... and finally no other value A1
Conclude \(x < \frac{4}{5}\) A1
Allow \(\left(-\infty, \frac{4}{5}\right)\)
Alternative Method:
Answer Marks
Guidance
Answer Mark
Guidance
State or imply non-modulus equation \((x-7)^2 = (4x+3)^2\) or inequality B1
Attempt solution of three-term quadratic equation or inequality M1
Obtain finally \(\frac{4}{5}\) only A1
Conclude \(x < \frac{4}{5}\) A1
Allow \(\left(-\infty, \frac{4}{5}\right)\)
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## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Attempt solution of equation or inequality, where signs of $x$ and $4x$ are different | M1 | |
| Obtain $\frac{4}{5}$ | A1 | OE |
| ... and finally no other value | A1 | |
| Conclude $x < \frac{4}{5}$ | A1 | Allow $\left(-\infty, \frac{4}{5}\right)$ |
**Alternative Method:**
| Answer | Mark | Guidance |
|--------|------|----------|
| State or imply non-modulus equation $(x-7)^2 = (4x+3)^2$ or inequality | B1 | |
| Attempt solution of three-term quadratic equation or inequality | M1 | |
| Obtain finally $\frac{4}{5}$ only | A1 | |
| Conclude $x < \frac{4}{5}$ | A1 | Allow $\left(-\infty, \frac{4}{5}\right)$ |
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2 Solve the inequality $| x - 7 | > 4 x + 3$.\\
\hfill \mbox{\textit{CAIE P2 2024 Q2 [4]}}