Question
Solve for \( n \) \[ \begin{array}{c}6 n-7(n+1)=6 n \\ n=\square \\ \text { Submit }\end{array} \]
Ask by Wells Ellis. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( n = -1 \)
Solution
Solve the equation \( 6n-7(n+1)=6n \).
Solve the equation by following steps:
- step0: Solve for \(n\):
\(6n-7\left(n+1\right)=6n\)
- step1: Cancel equal terms:
\(-7\left(n+1\right)=0\)
- step2: Change the sign:
\(7\left(n+1\right)=0\)
- step3: Rewrite the expression:
\(n+1=0\)
- step4: Move the constant to the right side:
\(n=0-1\)
- step5: Remove 0:
\(n=-1\)
The solution to the equation \(6n-7(n+1)=6n\) is \(n=-1\).
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Simplify this solution Extra Insights
To solve for \( n \), we start with the equation: \[ 6n - 7(n + 1) = 6n \] First, distribute the \(-7\) on the left-hand side: \[ 6n - 7n - 7 = 6n \] Now, combine like terms: \[ - n - 7 = 6n \] Next, add \( n \) to both sides to get all terms involving \( n \) on one side: \[ - 7 = 6n + n \] This simplifies to: \[ - 7 = 7n \] Now, divide both sides by \( 7 \): \[ n = -1 \] Thus, the solution is: \[ n = -1 \]
