To determine which expression represents [tex]\(PS\)[/tex], we need to combine the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We are looking to find the expression for [tex]\(PS\)[/tex], which is the sum of [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:
[tex]\[
PS = PR + RS
\][/tex]
Substitute the expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
Now, we combine the like terms:
1. Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
4x + 3x = 7x
\][/tex]
2. Combine the constant terms:
[tex]\[
-2 - 5 = -7
\][/tex]
Put it all together:
[tex]\[
PS = 7x - 7
\][/tex]
Thus, the expression that represents [tex]\(PS\)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
So, the correct option is:
[tex]\[ 7x - 7 \][/tex]
