To find the expression for [tex]\( PS \)[/tex], let's analyze the given expressions:
1. We are given that [tex]\( PR = 4x - 2 \)[/tex].
2. We are also given that [tex]\( RS = 3x - 5 \)[/tex].
We need to find the expression for [tex]\( PS \)[/tex]. According to geometrical properties, if [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] are consecutive segments of a line, [tex]\( PS \)[/tex] will be their sum. Therefore:
[tex]\[
PS = PR + RS
\][/tex]
Substituting the given expressions into this equation:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
Now, we 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].
Thus, the expression for [tex]\( PS \)[/tex] is:
[tex]\[
PS = 7x - 7
\][/tex]
Therefore, the correct expression that represents [tex]\( PS \)[/tex] is [tex]\( 7x - 7 \)[/tex].
Among the given options:
- [tex]\( x - 7 \)[/tex]
- [tex]\( x - 3 \)[/tex]
- [tex]\( 7x - 7 \)[/tex]
- [tex]\( 7x + 3 \)[/tex]
The correct answer is:
[tex]\[
7x - 7
\][/tex]
