For this case we have that the PS segment is given by the sum of the PR and RS segments. That is to say:
[tex]PS = PR + RS[/tex]
Where:
[tex]PR = 4x-2\\RS = 3x-5[/tex]
Adding we have:
[tex]PS = 4x-2 + (3x-5)\\PS = 4x-2 + 3x-5\\PS = 4x + 3x-2-5[/tex]
The same signs add up and the same sign is placed.
[tex]PS = 7x-7[/tex]
Answer:
[tex]PS = 7x-7[/tex]
Option C
