Solve 1/3n-1/4(6-n)=5/6

$$\frac { 1 } { 3 } n - \frac { 1 } { 4 } ( 6 - n ) = \frac { 5 } { 6 }$$

Solve for n

$$n=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{4} by 6-n.

$$\frac{1}{3}n-\frac{1}{4}\times 6-\frac{1}{4}\left(-1\right)n=\frac{5}{6}$$

Express -\frac{1}{4}\times 6 as a single fraction.

$$\frac{1}{3}n+\frac{-6}{4}-\frac{1}{4}\left(-1\right)n=\frac{5}{6}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}n-\frac{3}{2}-\frac{1}{4}\left(-1\right)n=\frac{5}{6}$$

Multiply -\frac{1}{4} and -1 to get \frac{1}{4}.

$$\frac{1}{3}n-\frac{3}{2}+\frac{1}{4}n=\frac{5}{6}$$

Combine \frac{1}{3}n and \frac{1}{4}n to get \frac{7}{12}n.

$$\frac{7}{12}n-\frac{3}{2}=\frac{5}{6}$$

Add \frac{3}{2} to both sides.

$$\frac{7}{12}n=\frac{5}{6}+\frac{3}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{7}{12}n=\frac{5}{6}+\frac{9}{6}$$

Since \frac{5}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}n=\frac{5+9}{6}$$

Add 5 and 9 to get 14.

$$\frac{7}{12}n=\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{12}n=\frac{7}{3}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$n=\frac{7}{3}\times \frac{12}{7}$$

Multiply \frac{7}{3} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{7\times 12}{3\times 7}$$

Cancel out 7 in both numerator and denominator.

$$n=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$n=4$$