To determine the expression representing [tex]\( PS \)[/tex], we start by noting that [tex]\( PS \)[/tex] consists of the combination of segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]. Thus, we can add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] together.
Given:
- [tex]\( PR = 4x - 2 \)[/tex]
- [tex]\( RS = 3x - 5 \)[/tex]
We need to find:
[tex]\[ PS = PR + RS \][/tex]
First, substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Next, combine the like terms:
1. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 4x + 3x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
Putting it all together, we get:
[tex]\[ PS = 7x - 7 \][/tex]
Therefore, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{7x - 7} \][/tex]
