To determine the expression representing [tex]\( PS \)[/tex], we'll start with the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
The total distance [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
Substituting the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Now we need to combine the like terms (terms with [tex]\( x \)[/tex] and the constant terms):
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 4x + 3x = 7x \][/tex]
Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
Therefore, combining both results:
[tex]\[ PS = 7x - 7 \][/tex]
So, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{7x - 7} \][/tex]
