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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
To determine the expression representing [tex]\( PS \)[/tex], we'll start with the given expressions for [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:

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

The total distance [tex]\( PS \)[/tex] is the sum of [tex]\( PR \)[/tex] and [tex]\( RS \)[/tex]:

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

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

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

Now we need to combine the like terms (terms with [tex]\( x \)[/tex] and the constant terms):

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

Combine the [tex]\( x \)[/tex] terms:

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

Combine the constant terms:

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

Therefore, combining both results:

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

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

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

Hence, the correct answer is:

[tex]\[ \boxed{7x - 7} \][/tex]
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