Moderate -0.8 This is a straightforward absolute value inequality requiring students to split into two cases (8-3x < 2 and 8-3x > -2) and solve two linear inequalities. It's a standard textbook exercise testing basic understanding of absolute values with minimal steps, making it easier than average but not trivial since it requires correct handling of inequality direction when dividing by negative coefficients.
EITHER: State or imply non-modular inequality e.g. \(-2 < 8-3x < 2\), or \((8-3x)^2 < 2^2\), or corresponding equation or pair of equations
M1
Obtain critical values \(2\) and \(3\frac{1}{3}\)
A1
State correct answer \(2 < x < 3\frac{1}{3}\)
A1
OR: State one critical value (probably \(x = 2\)), from a graphical method or by inspection or by solving a linear equality or equation
B1
State the other critical value correctly
B1
State correct answer \(2 < x < 3\frac{1}{3}\)
B1
Total: [3]
**EITHER:** State or imply non-modular inequality e.g. $-2 < 8-3x < 2$, or $(8-3x)^2 < 2^2$, or corresponding equation or pair of equations | M1 |
Obtain critical values $2$ and $3\frac{1}{3}$ | A1 |
State correct answer $2 < x < 3\frac{1}{3}$ | A1 |
**OR:** State one critical value (probably $x = 2$), from a graphical method or by inspection or by solving a linear equality or equation | B1 |
State the other critical value correctly | B1 |
State correct answer $2 < x < 3\frac{1}{3}$ | B1 |
**Total: [3]**