To find the expression for [tex]\( PS \)[/tex], we need to add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]
We want to find [tex]\( PS \)[/tex], which is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
First, write down the expressions to be added:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
Next, combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( 4x + 3x = 7x \)[/tex]
- Combine the constant terms: [tex]\( -2 - 5 = -7 \)[/tex]
So the expression for [tex]\( PS \)[/tex] becomes:
[tex]\[ PS = 7x - 7 \][/tex]
Thus, the correct expression for [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Therefore, the correct answer is:
[tex]\[ 7x - 7 \][/tex]
