Moderate -0.5 This is a straightforward modulus equation requiring students to consider cases where expressions are positive or negative, then solve resulting linear equations and check validity. It's slightly easier than average as it involves only linear expressions and standard case-by-case analysis with no geometric insight or complex algebraic manipulation required.
Either attempt to square both sides obtaining three terms on each side
M1
Attempt solution of three-term quadratic equation
M1
Obtain \(5x + 4x - 9 = 0\) and hence \(-\frac{9}{5}\) and \(1\)
A1
OR
Answer
Marks
Guidance
Obtain value \(1\) from graphical method, inspection or linear equation
B1
Obtain value \(-\frac{9}{5}\) similarly
B2
[3]
Either attempt to square both sides obtaining three terms on each side | M1 |
Attempt solution of three-term quadratic equation | M1 |
Obtain $5x + 4x - 9 = 0$ and hence $-\frac{9}{5}$ and $1$ | A1 |
OR
Obtain value $1$ from graphical method, inspection or linear equation | B1 |
Obtain value $-\frac{9}{5}$ similarly | B2 | [3]