To determine the expression for [tex]\(PS\)[/tex], we need to sum the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
The segment [tex]\(PS\)[/tex] is the sum of segments [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, combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
Simplify the expression:
[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]
Hence, the correct expression is:
[tex]\[ \boxed{7x - 7} \][/tex]
