Standard +0.3 This is a straightforward absolute value inequality requiring case analysis (considering signs of expressions inside absolute values) and solving linear inequalities in each case. While it requires systematic working through multiple cases, the algebraic manipulation is routine and this is a standard textbook exercise for A-level Pure Mathematics 2, making it slightly easier than average.
State or imply non-modular inequality \((2x - 3)^2 \leq (3x)^2\), or corresponding equation or pair of linear equations
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(-3\) and \(\frac{3}{5}\)
A1
State correct answer \(x \leq -3\) or \(x \geq \frac{3}{5}\)
A1
OR
Answer
Marks
Guidance
State one critical value, e.g. \(x = -3\), by solving a linear equation (or inequality) or from a graphical method or by inspection
B1
State the other critical value correctly
B2
State correct answer \(x \leq -3\) or \(x \geq \frac{3}{5}\)
B1
[4]
**EITHER**
State or imply non-modular inequality $(2x - 3)^2 \leq (3x)^2$, or corresponding equation or pair of linear equations | M1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $-3$ and $\frac{3}{5}$ | A1 |
State correct answer $x \leq -3$ or $x \geq \frac{3}{5}$ | A1 |
**OR**
State one critical value, e.g. $x = -3$, by solving a linear equation (or inequality) or from a graphical method or by inspection | B1 |
State the other critical value correctly | B2 |
State correct answer $x \leq -3$ or $x \geq \frac{3}{5}$ | B1 | [4]