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]
