To determine which expression represents [tex]\( PS \)[/tex], we need to add the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] together.
1. Given:
[tex]\[
PR = 4x - 2
\][/tex]
[tex]\[
RS = 3x - 5
\][/tex]
2. Add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = PR + RS = (4x - 2) + (3x - 5)
\][/tex]
3. Combine like terms:
[tex]\[
PS = 4x + 3x - 2 - 5
\][/tex]
4. Simplify the equation by combining the like terms [tex]\( 4x \)[/tex] and [tex]\( 3x \)[/tex]:
[tex]\[
PS = 7x - 2 - 5
\][/tex]
5. Combine the constant terms:
[tex]\[
PS = 7x - 7
\][/tex]
Therefore, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[
7x - 7
\][/tex]
So, the correct option is:
[tex]\[
\boxed{7x - 7}
\][/tex]
