Standard +0.3 This requires squaring both sides to eliminate moduli, expanding and simplifying a quadratic inequality, then factorizing to find critical values. While it involves multiple steps and careful algebraic manipulation, the technique is standard for C3 modulus inequalities and doesn't require novel insight—just systematic application of a well-practiced method.
For squaring both sides; For reduction to correct quadratic; For factorising, or equivalent; For both critical values correct; For completely correct solution set
OR:
Answer
Marks
Guidance
Critical values where \(2x + 1 = \pm(x - 1)\) i.e. where \(x = -2\) and \(x = 0\) Hence \(x < -2\) or \(x > 0\)
M1, B1, A1, M1, A1
For considering both cases, or from graphs; For the correct value \(-2\); For the correct value \(0\); For any correct method for solution set using two critical values; For completely correct solution set
$4x^2 + 4x + 1 > x^2 - 2x + 1$ i.e. $3x^2 + 6x > 0$ So $x(x + 2) > 0$ Hence $x < -2$ or $x > 0$ | M1, A1, M1, A1, A1 | For squaring both sides; For reduction to correct quadratic; For factorising, or equivalent; For both critical values correct; For completely correct solution set
**OR:**
Critical values where $2x + 1 = \pm(x - 1)$ i.e. where $x = -2$ and $x = 0$ Hence $x < -2$ or $x > 0$ | M1, B1, A1, M1, A1 | For considering both cases, or from graphs; For the correct value $-2$; For the correct value $0$; For any correct method for solution set using two critical values; For completely correct solution set
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