Pregunta
Which answer choice is equivalent to the expression below? \( -7(2+n)+\frac{1}{3}(-9-6 n) \) \( -17-9 n \) \( -14-12 n \) \( 11+5 n \) \( 14+2 n \)
Ask by Joseph Matthews. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The equivalent expression is \( -17 - 9n \).
Solución
To determine which answer choice is equivalent to the expression \( -7(2 + n) + \frac{1}{3}(-9 - 6n) \), let's simplify the expression step by step.
1. **Distribute the \(-7\) in the first term:**
\[
-7(2 + n) = -7 \times 2 + (-7) \times n = -14 - 7n
\]
2. **Distribute the \(\frac{1}{3}\) in the second term:**
\[
\frac{1}{3}(-9 - 6n) = \frac{1}{3} \times (-9) + \frac{1}{3} \times (-6n) = -3 - 2n
\]
3. **Combine the two results:**
\[
-14 - 7n + (-3) - 2n = (-14 - 3) + (-7n - 2n) = -17 - 9n
\]
So, the simplified expression is \( -17 - 9n \).
**Answer Choice:**
\[ \boxed{-17-9 n} \]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
First, let's simplify the expression \( -7(2+n)+\frac{1}{3}(-9-6 n) \). Distributing the \( -7 \) gives us \( -14 - 7n \). Now, for the second part, we distribute \( \frac{1}{3} \) through \( (-9-6n) \), which results in \( -3 - 2n \). Combining these results, we have: \[ -14 - 7n - 3 - 2n = -17 - 9n \] So, the expression simplifies to \( -17 - 9n \). This matches with the answer choice \( -17-9 n \) perfectly. Now you know how to work through distributing and combining like terms! How cool is math when all you need is a little bit of organization and systematic thinking? Keep practicing, and soon, you’ll be a whiz at simplifying expressions!
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