Moderate -0.3 This is a straightforward modulus inequality requiring students to consider two cases (x ≥ 3 and x < 3) and solve linear inequalities in each case. While it requires understanding of the modulus function definition, the algebraic manipulation is routine and the question is slightly easier than a typical A-level question due to its single-step nature and standard technique application.
State or imply non-modular inequality \((2-3x)^2 < (x-3)^2\), or corresponding equation, and make a reasonable solution attempt at a 3-term quadratic
M1
Obtain critical value \(x = -\frac{1}{2}\)
A1
Obtain \(x > -\frac{1}{2}\)
A1
Fully justify \(x > -\frac{1}{2}\) as only answer
A1
[4]
OR1:
Answer
Marks
State the relevant critical linear equation, i.e. \(2 - 3x = 3 - x\)
B1
Obtain critical value \(x = -\frac{1}{2}\)
B1
Obtain \(x > -\frac{1}{2}\)
B1
Fully justify \(x > -\frac{1}{2}\) as only answer
B1
OR2:
Answer
Marks
Obtain the critical value \(x = -\frac{1}{2}\) by inspection, or by solving a linear inequality
B2
Obtain \(x > -\frac{1}{2}\)
B1
Fully justify \(x > -\frac{1}{2}\) as only answer
B1
OR3:
Answer
Marks
Make recognisable sketches of \(y = 2 - 3x\) and \(y = \lvert x - 3 \rvert\) on a single diagram
B1
Obtain critical value \(x = -\frac{1}{2}\)
B1
Obtain \(x > -\frac{1}{2}\)
B1
Fully justify \(x > -\frac{1}{2}\) as only answer
B1
[Condone \(\geq\) for \(>\) in the third mark but not the fourth.]
| State or imply non-modular inequality $(2-3x)^2 < (x-3)^2$, or corresponding equation, and make a reasonable solution attempt at a 3-term quadratic | M1 |
| Obtain critical value $x = -\frac{1}{2}$ | A1 |
| Obtain $x > -\frac{1}{2}$ | A1 |
| Fully justify $x > -\frac{1}{2}$ as only answer | A1 |
| [4] |
**OR1:**
| State the relevant critical linear equation, i.e. $2 - 3x = 3 - x$ | B1 |
| Obtain critical value $x = -\frac{1}{2}$ | B1 |
| Obtain $x > -\frac{1}{2}$ | B1 |
| Fully justify $x > -\frac{1}{2}$ as only answer | B1 |
**OR2:**
| Obtain the critical value $x = -\frac{1}{2}$ by inspection, or by solving a linear inequality | B2 |
| Obtain $x > -\frac{1}{2}$ | B1 |
| Fully justify $x > -\frac{1}{2}$ as only answer | B1 |
**OR3:**
| Make recognisable sketches of $y = 2 - 3x$ and $y = \lvert x - 3 \rvert$ on a single diagram | B1 |
| Obtain critical value $x = -\frac{1}{2}$ | B1 |
| Obtain $x > -\frac{1}{2}$ | B1 |
| Fully justify $x > -\frac{1}{2}$ as only answer | B1 |
| [Condone $\geq$ for $>$ in the third mark but not the fourth.] |