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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 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]

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