Question
Solve for \( n \) \( 2(n-7)-5=-1 \) \( n=\square \)
Ask by Gonzalez Guzman. in the United States
Jan 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( n = 9 \)
Solution
To solve the equation \( 2(n - 7) - 5 = -1 \) for \( n \), follow these steps:
1. **Expand the equation:**
\[
2(n - 7) - 5 = -1 \\
2n - 14 - 5 = -1
\]
2. **Combine like terms:**
\[
2n - 19 = -1
\]
3. **Isolate \( n \):**
\[
2n = -1 + 19 \\
2n = 18 \\
n = \frac{18}{2} \\
n = 9
\]
**Answer:**
\[
n = 9
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
First, let's start solving the equation step by step. We have: \[ 2(n-7) - 5 = -1 \] Distributing the 2 gives us: \[ 2n - 14 - 5 = -1 \] Combine the constants: \[ 2n - 19 = -1 \] Next, we add 19 to both sides: \[ 2n = 18 \] Dividing both sides by 2, we find: \[ n = 9 \] So, \( n = 9 \). 🎉 Now, remember, equations like this involve isolating the variable! A common mistake is to forget to distribute properly or combine like terms efficiently. Always keep an eye on those negative signs too—they can sneak up on you! Also, check your final solution by plugging \( n \) back into the original equation to verify your answer is correct!
