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

A. [tex][tex]$x - 7$[/tex][/tex]

B. [tex]$x - 3$[/tex]

C. [tex]$7x - 7$[/tex]

D. [tex][tex]$7x + 3$[/tex][/tex]

Sagot :

GinnyAnsweridn
To determine which expression represents [tex]\( PS \)[/tex] when given [tex]\( PR = 4x - 2 \)[/tex] and [tex]\( RS = 3x - 5 \)[/tex], let's walk through the steps:

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

2. Calculate [tex]\( PS \)[/tex] by adding [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] into the equation for [tex]\( PS \)[/tex]:
[tex]\[ PS = (4x - 2) + (3x - 5) \][/tex]

4. Combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]

5. Simplify the expression:
[tex]\[ PS = 7x - 7 \][/tex]

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

The correct answer is:
[tex]\[ 7x - 7 \][/tex]
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