To find the expression that represents [tex]\( PS \)[/tex], we need to sum the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
The segment [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
Let's substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Now, we combine like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ \boxed{7x - 7} \][/tex]
So, the correct answer is [tex]\(7x - 7\)[/tex].
