To determine which expression represents [tex]\( PS \)[/tex] when given [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], let's walk through the steps:
1. Identify the given expressions:
- [tex]\( PR = 4x - 2 \)[/tex]
- [tex]\( RS = 3x - 5 \)[/tex]
2. Calculate [tex]\( PS \)[/tex] by adding [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = PR + RS
\][/tex]
3. Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] into the equation for [tex]\( PS \)[/tex]:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
4. Combine the like terms:
[tex]\[
PS = 4x + 3x - 2 - 5
\][/tex]
5. Simplify the expression:
[tex]\[
PS = 7x - 7
\][/tex]
So, the expression that represents [tex]\( PS \)[/tex] is [tex]\( 7x - 7 \)[/tex].
The correct answer is:
[tex]\[ 7x - 7 \][/tex]
