To determine the expression for [tex]\( PS \)[/tex], we start by understanding that [tex]\( PS \)[/tex] is the sum of the two segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
To find [tex]\( PS \)[/tex], we add [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Next, we combine like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
Simplifying the expression:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Therefore, the correct answer is:
[tex]\[ 7x - 7 \][/tex]
