solve for n.\n$\frac{1}{12}n + 2=\frac{7}{12}n - 3+\frac{5}{6}n$\n$n = square$

Explanation:

Step1: Combine like - terms on the right side

First, find a common denominator for the $n$ terms on the right side. The common denominator of 12 and 6 is 12. So $\frac{5}{6}n=\frac{10}{12}n$. Then $\frac{7}{12}n+\frac{5}{6}n - \frac{1}{12}n=\frac{7 + 10-1}{12}n=\frac{16}{12}n=\frac{4}{3}n$. The equation becomes $\frac{1}{12}n+2=\frac{4}{3}n - 3$.

Step2: Move $n$ terms to one side

Subtract $\frac{1}{12}n$ from both sides: $2=\frac{4}{3}n-\frac{1}{12}n - 3$. Then find a common denominator for the $n$ terms on the right side again. $\frac{4}{3}n=\frac{16}{12}n$, so $\frac{16}{12}n-\frac{1}{12}n=\frac{15}{12}n=\frac{5}{4}n$. The equation is now $2=\frac{5}{4}n - 3$.

Step3: Isolate the $n$ term

Add 3 to both sides: $2 + 3=\frac{5}{4}n$, so $5=\frac{5}{4}n$.

Step4: Solve for $n$

Multiply both sides by $\frac{4}{5}$ to get $n = 4$.

Answer:

$4$