QuestionAugust 26, 2025

Solve for n. (1)/(12)n+2=(7)/(12)n-3+(5)/(6)n n= disappointed square

Solve for n. (1)/(12)n+2=(7)/(12)n-3+(5)/(6)n n= disappointed square
Solve for n.
(1)/(12)n+2=(7)/(12)n-3+(5)/(6)n
n= disappointed square

Solution
4.1(206 votes)

Answer

n = \frac{15}{4} Explanation 1. Combine like terms Combine \frac{1}{12}n, \frac{7}{12}n, and \frac{5}{6}n. Convert \frac{5}{6} to \frac{10}{12} for a common denominator. The equation becomes \frac{1}{12}n + 2 = \left(\frac{7}{12} + \frac{10}{12}\right)n - 3. 2. Simplify the equation Simplify the right side: \frac{17}{12}n - 3. The equation is now \frac{1}{12}n + 2 = \frac{17}{12}n - 3. 3. Isolate n Subtract \frac{1}{12}n from both sides: 2 = \frac{16}{12}n - 3. Simplify \frac{16}{12} to \frac{4}{3}, so 2 = \frac{4}{3}n - 3. 4. Solve for n Add 3 to both sides: 5 = \frac{4}{3}n. Multiply both sides by \frac{3}{4} to solve for n: n = 5 \times \frac{3}{4}.

Explanation

1. Combine like terms<br /> Combine $\frac{1}{12}n$, $\frac{7}{12}n$, and $\frac{5}{6}n$. Convert $\frac{5}{6}$ to $\frac{10}{12}$ for a common denominator. The equation becomes $\frac{1}{12}n + 2 = \left(\frac{7}{12} + \frac{10}{12}\right)n - 3$.<br />2. Simplify the equation<br /> Simplify the right side: $\frac{17}{12}n - 3$. The equation is now $\frac{1}{12}n + 2 = \frac{17}{12}n - 3$.<br />3. Isolate n<br /> Subtract $\frac{1}{12}n$ from both sides: $2 = \frac{16}{12}n - 3$. Simplify $\frac{16}{12}$ to $\frac{4}{3}$, so $2 = \frac{4}{3}n - 3$.<br />4. Solve for n<br /> Add 3 to both sides: $5 = \frac{4}{3}n$. Multiply both sides by $\frac{3}{4}$ to solve for $n$: $n = 5 \times \frac{3}{4}$.
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