To determine which expression represents [tex]\( PS \)[/tex], you 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]
We want to find [tex]\( PS \)[/tex], which is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = PR + RS
\][/tex]
Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
Combine like terms:
[tex]\[
PS = 4x + 3x - 2 - 5
\][/tex]
[tex]\[
PS = 7x - 7
\][/tex]
Therefore, the expression that represents [tex]\( PS \)[/tex] is [tex]\( 7x - 7 \)[/tex].
So, the correct answer is:
[tex]\[
7x - 7
\][/tex]
