To find the expression for [tex]\( PS \)[/tex] given that [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], we need to add the two expressions together.
First, let's start by writing down the two expressions:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
Next, we combine the two expressions by adding them together:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Now, we will combine like terms:
1. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 4x + 3x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]
Putting it all together, we get:
[tex]\[ PS = 7x - 7 \][/tex]
Therefore, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
So the correct answer is:
[tex]\[ \boxed{7x - 7} \][/tex]
