Easy -1.2 This is a straightforward application of the basic modulus inequality rule: |expression| < k means -k < expression < k. Students simply need to recall this definition, set up -3 < 4-5x < 3, and solve two linear inequalities. It requires minimal problem-solving and is a standard textbook exercise testing routine technique.
State or imply non-modular inequality \((4-5x)^2 < 3^2\), or corresponding equation or pair of linear equations
M1
Obtain critical values \(\frac{1}{5}\) and \(\frac{7}{5}\)
A1
State correct answer \(\frac{1}{5} < x < \frac{7}{5}\)
A1
OR
Answer
Marks
Guidance
State one critical value, e.g. \(x = \frac{1}{5}\), by solving a linear equation (or inequality) or from a graphical method or by inspection
B1
State the other critical value correctly
B1
State correct answer \(\frac{1}{5} < x < \frac{7}{5}\)
B1
[3]
State or imply non-modular inequality $(4-5x)^2 < 3^2$, or corresponding equation or pair of linear equations | M1 |
Obtain critical values $\frac{1}{5}$ and $\frac{7}{5}$ | A1 |
State correct answer $\frac{1}{5} < x < \frac{7}{5}$ | A1 |
**OR**
State one critical value, e.g. $x = \frac{1}{5}$, by solving a linear equation (or inequality) or from a graphical method or by inspection | B1 |
State the other critical value correctly | B1 |
State correct answer $\frac{1}{5} < x < \frac{7}{5}$ | B1 | [3]