Answered

If [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], which expression represents [tex]\( PS \)[/tex]?

A. [tex]\( x - 7 \)[/tex]
B. [tex]\( x - 3 \)[/tex]
C. [tex]\( 7x - 7 \)[/tex]
D. [tex]\( 7x + 3 \)[/tex]



Answer :

GinnyAnswer
To determine 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 [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].

Let's proceed step-by-step:

1. Write down the given expressions:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]

2. To find [tex]\( PS \)[/tex], add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]

3. Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]

4. Combine the like terms (terms involving [tex]\( x \)[/tex] with terms involving [tex]\( x \)[/tex], and constant terms with constant terms):
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]

5. Simplify the expression:
[tex]\[ PS = (4x + 3x) + (-2 - 5) \][/tex]
[tex]\[ PS = 7x - 7 \][/tex]

So, the expression that represents [tex]\( PS \)[/tex] is:
[tex]\[ 7x - 7 \][/tex]

Therefore, the correct option is:

[tex]\[ \boxed{7x - 7} \][/tex]

Other Questions