To find the expression for [tex]\( PS \)[/tex] given [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], we need to add the two expressions together because [tex]\( PS \)[/tex] represents the combined length of segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
Step-by-step solution:
1. Write down the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
- [tex]\( PR = 4x - 2 \)[/tex]
- [tex]\( RS = 3x - 5 \)[/tex]
2. Add these two expressions to find [tex]\( PS \)[/tex]:
[tex]\[
PS = PR + RS
\][/tex]
3. Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
4. Combine like terms:
- Add the terms involving [tex]\( x \)[/tex]:
[tex]\[
4x + 3x = 7x
\][/tex]
- Add the constant terms:
[tex]\[
-2 - 5 = -7
\][/tex]
5. Therefore, the combined expression for [tex]\( PS \)[/tex] is:
[tex]\[
PS = 7x - 7
\][/tex]
The result is:
[tex]\[
7x - 7
\][/tex]
So, the correct expression that represents [tex]\( PS \)[/tex] is [tex]\( 7x - 7 \)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{7x - 7}
\][/tex]
