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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]

Sagot :

GinnyAnswer
To determine the expression for [tex]\( PS \)[/tex], we start by understanding that [tex]\( PS \)[/tex] is the sum of the two segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].

Given:
[tex]\[ PR = 4x - 2 \][/tex]
[tex]\[ RS = 3x - 5 \][/tex]

To find [tex]\( PS \)[/tex], we add [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:
[tex]\[ PS = PR + RS \][/tex]
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]

Next, we combine like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]

Simplifying the expression:
[tex]\[ PS = 7x - 7 \][/tex]

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

Therefore, the correct answer is:
[tex]\[ 7x - 7 \][/tex]
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