Standard +0.3 This requires squaring both sides to eliminate moduli, expanding and simplifying a quadratic inequality, then factorizing to find the solution set. It's slightly above average difficulty as it involves multiple algebraic steps and understanding that squaring preserves the inequality direction for positive expressions, but it's a standard technique taught in P2 with no novel insight required.
EITHER: Obtain a non-modular inequality from \(2x + 3)^2 < (x - 3)^2\), or corresponding quadratic equation, or pair of linear equations \(2x + 3 = \pm(x - 3)\)
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(x = -6\) and \(x = 0\)
A1
State answer \(-6 < x < 0\)
A1
OR: Obtain the critical value \(x = -6\) from a graphical method or by inspection, or by solving a linear equation or inequality
B1
Obtain the critical value \(x = 0\) similarly
B2
State answer \(-6 < x < 0\)
B1
[4 marks]
**EITHER:** Obtain a non-modular inequality from $2x + 3)^2 < (x - 3)^2$, or corresponding quadratic equation, or pair of linear equations $2x + 3 = \pm(x - 3)$ | M1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $x = -6$ and $x = 0$ | A1 |
State answer $-6 < x < 0$ | A1 |
**OR:** Obtain the critical value $x = -6$ from a graphical method or by inspection, or by solving a linear equation or inequality | B1 |
Obtain the critical value $x = 0$ similarly | B2 |
State answer $-6 < x < 0$ | B1 | [4 marks]