To solve the expression [tex]\(-7(2+n) + \frac{1}{3}(-9-6n)\)[/tex], we will simplify each part step-by-step.
Step 1: Simplify the first part: [tex]\( -7(2+n) \)[/tex]
Distribute [tex]\( -7 \)[/tex] to both terms inside the parenthesis:
[tex]\[
-7(2+n) = -7 \cdot 2 + (-7) \cdot n = -14 - 7n
\][/tex]
Step 2: Simplify the second part: [tex]\(\frac{1}{3}(-9-6n)\)[/tex]
Distribute [tex]\(\frac{1}{3}\)[/tex] to both terms inside the parenthesis:
[tex]\[
\frac{1}{3}(-9-6n) = \frac{1}{3} \cdot (-9) + \frac{1}{3} \cdot (-6n) = -3 - 2n
\][/tex]
Step 3: Combine the results of the two parts:
Now add [tex]\(-14 - 7n\)[/tex] and [tex]\(-3 - 2n\)[/tex]:
[tex]\[
-14 - 7n + (-3 - 2n)
\][/tex]
Combine the like terms (constants with constants and coefficients of [tex]\(n\)[/tex] with coefficients of [tex]\(n\)[/tex]):
[tex]\[
-14 - 3 + (-7n - 2n) = -17 - 9n
\][/tex]
Thus, the expression simplifies to:
[tex]\[
-17 - 9n
\][/tex]
So the equivalent expression is:
[tex]\(-17 - 9n\)[/tex]
Therefore, the correct answer is [tex]\(\boxed{-17-9n}\)[/tex].
