Moderate -0.8 This is a straightforward modulus equation requiring students to consider cases where expressions inside the modulus are positive or negative. The method is standard (square both sides or consider sign cases), and the algebra is simple with linear expressions only, making it easier than average but not trivial since it requires systematic case analysis.
Form linear equation with signs of \(6x\) and \(x\) different
M1
[ignoring other sign errors]
State \(6x - 1 = -x + 1\)
A1
[or correct equiv with or without brackets]
Obtain \(\frac{2}{7}\) and no other non-zero value
A1
Total: 4 marks [or exact equiv]
Or: Obtain \(36x^2 - 12x + 1 = x^2 - 2x + 1\)
B1
[or equiv]
Attempt to solve quadratic equation
M1
[as far as factorisation or subn into formula]
Obtain \(\frac{2}{7}\) and no other non-zero value
A1
[or exact equiv]
Obtain 0
B1
Total: 4 marks [ignoring errors in working]
Either obtain $x = 0$ | B1 | [ignoring errors in working]
Form linear equation with signs of $6x$ and $x$ different | M1 | [ignoring other sign errors]
State $6x - 1 = -x + 1$ | A1 | [or correct equiv with or without brackets]
Obtain $\frac{2}{7}$ and no other non-zero value | A1 | Total: 4 marks [or exact equiv]
Or: Obtain $36x^2 - 12x + 1 = x^2 - 2x + 1$ | B1 | [or equiv]
Attempt to solve quadratic equation | M1 | [as far as factorisation or subn into formula]
Obtain $\frac{2}{7}$ and no other non-zero value | A1 | [or exact equiv]
Obtain 0 | B1 | Total: 4 marks [ignoring errors in working]