Answered

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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 determine which expression represents [tex]\(PS\)[/tex], we need to combine the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex].

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

We are looking to find the expression for [tex]\(PS\)[/tex], which is the sum of [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:

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

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

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

Now, we combine the like terms:

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

2. Combine the constant terms:
[tex]\[ -2 - 5 = -7 \][/tex]

Put it all together:

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

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

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

So, the correct option is:

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