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Simplify to create an equivalent expression.

[tex]\[ 2(3r + 7) - (2 + r) \][/tex]

Choose one answer:

A. [tex]\[ 4r + 12 \][/tex]
B. [tex]\[ 5r + 13 \][/tex]
C. [tex]\[ 5r + 12 \][/tex]
D. [tex]\[ 5r - 12 \][/tex]

Sagot :

GinnyAnsweridn
Certainly! To simplify the expression:

[tex]\[ 2(3r + 7) - (2 + r) \][/tex]

Follow these steps:

1. Distribute the [tex]\(2\)[/tex] within the first parenthesis:
[tex]\[ 2 \cdot 3r + 2 \cdot 7 = 6r + 14 \][/tex]

2. Distribute the [tex]\(-1\)[/tex] within the second parenthesis:
[tex]\[ -(2 + r) = -2 - r \][/tex]

3. Combine the results from steps 1 and 2:
[tex]\[ 6r + 14 - 2 - r \][/tex]

4. Combine the like terms (terms involving [tex]\(r\)[/tex] and constant terms):
[tex]\[ 6r - r = 5r \][/tex]
[tex]\[ 14 - 2 = 12 \][/tex]

5. Combine these simplified parts:
[tex]\[ 5r + 12 \][/tex]

Thus, the simplified expression is:

[tex]\[ 5r + 12 \][/tex]

So, the correct answer is:
(C) [tex]\(5r + 12\)[/tex]
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