Standard +0.3 This is a standard modulus inequality requiring consideration of critical points (x = 1/3 and x = -5/2) and testing intervals, but follows a routine method taught explicitly in P3. It's slightly above average difficulty due to the algebraic manipulation across multiple cases, but remains a textbook exercise with no novel insight required.
State or imply non-modular inequality \((3x-1)^2 < (2x+5)^2\) or corresponding quadratic equation or pair of linear equations \(3x-1 = \pm(2x+5)\)
B1
Solve a three-term quadratic or two linear equations \(5x^2 - 26x - 24 < 0\)
M1
Obtain \(-\frac{4}{5}\) and \(6\)
A1
State \(-\frac{4}{5} < x < 6\)
A1
[4]
Or route:
Answer
Marks
Guidance
Obtain value \(6\) from graph, inspection or solving linear equation
B1
Obtain value \(-\frac{4}{5}\) similarly
B2
State \(-\frac{4}{5} < x < 6\)
B1
[4]
**Either route:**
State or imply non-modular inequality $(3x-1)^2 < (2x+5)^2$ or corresponding quadratic equation or pair of linear equations $3x-1 = \pm(2x+5)$ | B1 |
Solve a three-term quadratic or two linear equations $5x^2 - 26x - 24 < 0$ | M1 |
Obtain $-\frac{4}{5}$ and $6$ | A1 |
State $-\frac{4}{5} < x < 6$ | A1 | [4]
**Or route:**
Obtain value $6$ from graph, inspection or solving linear equation | B1 |
Obtain value $-\frac{4}{5}$ similarly | B2 |
State $-\frac{4}{5} < x < 6$ | B1 | [4]