A-Level Maths B7-12 Graphs: Examples of Solving Basic Modulus Inequalities

[MathBuz]

Thank you very much for your great efforts.

In Question 3:
Even if we solve it without changing the 8 - 4x to 4x - 8, its not very difficult
- 7 < 8 - 4x < 7
-15 < -4x < -1
15/4 > x > 1/4
even if we write
1/4 < x < 15/4
Can you please clear your view point that how mistakes may done?

[sophiekelly]

Why on number 3 if I kept it as 8-4x I get the same answer but the wrong way round as in 15/4<x<1/4