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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 :

GinnyAnsweridn
Let's solve the problem step-by-step:

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

We need to find the expression that represents [tex]\( PS \)[/tex], where [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex].

To combine [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:

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

Substitute the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:

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

Now, let's simplify this combined expression step-by-step:

1. Combine the like terms involving [tex]\( x \)[/tex]:

[tex]\[ 4x + 3x = 7x \][/tex]

2. Combine the constant terms:

[tex]\[ -2 - 5 = -7 \][/tex]

So, the simplified expression for [tex]\( PS \)[/tex]:

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

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

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

Given the options listed:

- [tex]\( x - 7 \)[/tex]
- [tex]\( x - 3 \)[/tex]
- [tex]\( 7x - 7 \)[/tex]
- [tex]\( 7x + 3 \)[/tex]

The correct option is:

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

Hence, the correct choice is the third one.
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