Let's solve the problem step-by-step:
Given two expressions:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We need to find the expression that represents [tex]\( PS \)[/tex], where [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
To combine [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]
Now, let's simplify this combined expression step-by-step:
1. Combine the like terms involving [tex]\( x \)[/tex]:
[tex]\[ 4x + 3x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
So, the simplified expression for [tex]\( PS \)[/tex]:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Given the options listed:
- [tex]\( x - 7 \)[/tex]
- [tex]\( x - 3 \)[/tex]
- [tex]\( 7x - 7 \)[/tex]
- [tex]\( 7x + 3 \)[/tex]
The correct option is:
[tex]\[ 7x - 7 \][/tex]
Hence, the correct choice is the third one.
