Answered

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If [tex][tex]$PR = 4x - 2$[/tex][/tex] and [tex][tex]$RS = 3x - 5$[/tex][/tex], which expression represents [tex][tex]$PS$[/tex][/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 representing [tex]\( PS \)[/tex], we start by noting that [tex]\( PS \)[/tex] consists of the combination of segments [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]. Thus, we can add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] together.

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

We need to find:
[tex]\[ PS = PR + RS \][/tex]

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

Next, combine the like terms:
1. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 4x + 3x = 7x \][/tex]

2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]

Putting it all together, we get:
[tex]\[ PS = 7x - 7 \][/tex]

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

Thus, the correct choice is:
[tex]\[ \boxed{7x - 7} \][/tex]
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