To determine the expression for [tex]\( PS \)[/tex] given the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex], follow these steps:
1. Write Down the Given Expressions:
[tex]\[
PR = 4x - 2
\][/tex]
[tex]\[
RS = 3x - 5
\][/tex]
2. Determine [tex]\( PS \)[/tex] by Adding [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
Since [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex], we can find [tex]\( PS \)[/tex] by adding the two expressions.
[tex]\[
PS = PR + RS
\][/tex]
Substituting the given expressions:
[tex]\[
PS = (4x - 2) + (3x - 5)
\][/tex]
3. Combine Like Terms:
First, combine the terms with [tex]\( x \)[/tex]:
[tex]\[
4x + 3x = 7x
\][/tex]
Next, combine the constant terms:
[tex]\[
-2 - 5 = -7
\][/tex]
So, the expression for [tex]\( PS \)[/tex] is:
[tex]\[
PS = 7x - 7
\][/tex]
4. Check the Provided Options:
Compare [tex]\( PS = 7x - 7 \)[/tex] with the provided options:
- [tex]\( x - 7 \)[/tex]
- [tex]\( x - 3 \)[/tex]
- [tex]\( 7x - 7 \)[/tex]
- [tex]\( 7x + 3 \)[/tex]
The expression [tex]\( PS = 7x - 7 \)[/tex] matches the third option.
Therefore, the correct expression for [tex]\( PS \)[/tex] is:
[tex]\[
\boxed{7x - 7}
\][/tex]
