Standard +0.3 This is a straightforward absolute value inequality requiring case analysis (x ≥ 7 and x < 7), solving two linear inequalities, and checking validity of solutions. It's slightly above average difficulty due to the need for systematic case work and careful attention to which solutions are valid in each case, but remains a standard textbook exercise with no novel insight required.
Attempt solution of equation or inequality, where signs of x and 4x are different
M1
Obtain 4 …
Answer
Marks
Guidance
5
A1
OE
… and finally no other value
A1
Conclude x 4
Answer
Marks
Guidance
5
A1
4
Allow −, .
5
Alternative Method for Question 2
Answer
Marks
State or imply non-modulus equation (x−7)2 =(4x+3)2 or inequality
B1
Attempt solution of three-term quadratic equation or inequality
M1
Obtain finally 4 only
Answer
Marks
5
A1
Conclude x 4
Answer
Marks
Guidance
5
A1
4
Allow −,
5
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Attempt solution of equation or inequality, where signs of x and 4x are different | M1
Obtain 4 …
5 | A1 | OE
… and finally no other value | A1
Conclude x 4
5 | A1 | 4
Allow −, .
5
Alternative Method for Question 2
State or imply non-modulus equation (x−7)2 =(4x+3)2 or inequality | B1
Attempt solution of three-term quadratic equation or inequality | M1
Obtain finally 4 only
5 | A1
Conclude x 4
5 | A1 | 4
Allow −,
5
4
Question | Answer | Marks | Guidance