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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
Sure! We are given the expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:

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

To find the expression for [tex]\(PS\)[/tex], we need to add [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]. Let's perform the addition step by step:

1. Start with the given expressions for [tex]\(PR\)[/tex] and [tex]\(RS\)[/tex]:

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

2. Add the expressions together:

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

3. Combine the like terms:

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

4. So, the expression for [tex]\(PS\)[/tex] becomes:

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

Thus, the expression that represents [tex]\(PS\)[/tex] is [tex]\(\boxed{7x - 7}\)[/tex].
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