When will the tension the same throughout a rope?

[Clara Chung]

Homework Statement

Homework Equations

The Attempt at a Solution

I have the solution of the questions and I don't understand why the tension in Q7 is assumed to be uniform throughout the rope, however the tension in Q7 is not the same throughout the rope (i.e. for a segment dl, the tension in each side is T(x+dx) and T(x) respectively.)
Thank you for your help.

 

[haruspex]

why the tension in Q7 is assumed to be uniform throughout the rope

If the string is massless and there is no friction then the tension must be constant. If not, the string segment would shift in the direction of the greater tension.