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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 for [tex]\(PS\)[/tex], we need to sum the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex].

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

The segment [tex]\(PS\)[/tex] is the sum of segments [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, combine the like terms:
[tex]\[ PS = 4x + 3x - 2 - 5 \][/tex]

Simplify the expression:
[tex]\[ PS = (4x + 3x) - (2 + 5) \][/tex]
[tex]\[ PS = 7x - 7 \][/tex]

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

Hence, the correct expression is:
[tex]\[ \boxed{7x - 7} \][/tex]