To determine the expression that represents [tex]\( PS \)[/tex], given that [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], we need to find [tex]\( PS \)[/tex] by adding the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
1. First, let's write down the given expressions:
- [tex]\( PR = 4x - 2 \)[/tex]
- [tex]\( RS = 3x - 5 \)[/tex]
2. To find [tex]\( PS \)[/tex], we add [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = PR + RS
\][/tex]
Substituting the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] into the equation, we get:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
3. Next, we combine like terms in the expression:
[tex]\[
PS = 4x + 3x - 2 - 5
\][/tex]
4. Simplifying this, we combine the coefficients of [tex]\( x \)[/tex]:
[tex]\[
4x + 3x = 7x
\][/tex]
5. We also combine the constant terms:
[tex]\[
-2 - 5 = -7
\][/tex]
6. Therefore, the simplified expression for [tex]\( PS \)[/tex] is:
[tex]\[
PS = 7x - 7
\][/tex]
Hence, the correct expression that represents [tex]\( PS \)[/tex] is [tex]\( \boxed{7x - 7} \)[/tex].
