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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], let's analyze the given expressions:

1. We are given that [tex]\( PR = 4x - 2 \)[/tex].
2. We are also given that [tex]\( RS = 3x - 5 \)[/tex].

We need to find the expression for [tex]\( PS \)[/tex]. According to geometrical properties, if [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex] are consecutive segments of a line, [tex]\( PS \)[/tex] will be their sum. Therefore:

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

Substituting the given expressions into this equation:

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

Now, we combine like terms:

1. Combine the [tex]\( x \)[/tex]-terms: [tex]\( 4x + 3x = 7x \)[/tex].
2. Combine the constant terms: [tex]\( -2 - 5 = -7 \)[/tex].

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

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

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

Among the given options:

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

The correct answer is:

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