Let's work through the given expressions step by step to determine which one represents [tex]\( PS \)[/tex].
You are given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
To find the expression for [tex]\( PS \)[/tex], you need to add [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
Substitute the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] into the equation:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Now, combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
So, the correct answer is:
[tex]\[ 7x - 7 \][/tex]
