To find the expression for [tex]\(PS\)[/tex], we first need to understand that [tex]\(PS\)[/tex] is the sum of [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We add these two expressions to get [tex]\(PS\)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Now we combine like terms in the expression:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]
Add the [tex]\(x\)[/tex]-terms and the constant terms separately:
[tex]\[ PS = (4x + 3x) + (-2 - 5) \][/tex]
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the expression that represents [tex]\(PS\)[/tex] is:
[tex]\[ PS = 7x - 7 \][/tex]
Therefore, the correct answer is:
[tex]\[ 7x - 7 \][/tex]
Since none of the provided options matches exactly, it appears there might be a slight discrepancy or typo in the options listed in the problem. In standard practice, the closest of the given options should be chosen, but in this case, the specific result derived correctly as per the given problem is [tex]\( 7x - 7 \)[/tex].
