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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 find the expression for [tex]\( PS \)[/tex], we need to add the expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].

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

We want to find [tex]\( PS \)[/tex], which is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:

[tex]\[ PS = PR + RS \][/tex]

First, write down the expressions to be added:

[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]

Next, combine like terms:

- 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] becomes:

[tex]\[ PS = 7x - 7 \][/tex]

Thus, the correct expression for [tex]\( PS \)[/tex] is:

[tex]\[ 7x - 7 \][/tex]

Therefore, the correct answer is:

[tex]\[ 7x - 7 \][/tex]
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