To find the expression for [tex]\( PS \)[/tex] given [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], follow these steps:
1. Understand that [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].
2. Add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]
3. Combine the like terms in the expression:
- 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] will be:
[tex]\[ PS = 7x - 7 \][/tex]
Therefore, the correct expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]
Among the given options, the correct one is:
[tex]\[ 7x - 7 \][/tex]
