Solve 1/3(y-3)-1/4(y-4)=1/6

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

Solve for y

$$y=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by y-3.

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

Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.

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

Divide -3 by 3 to get -1.

$$\frac{1}{3}y-1-\frac{1}{4}\left(y-4\right)=\frac{1}{6}$$

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

$$\frac{1}{3}y-1-\frac{1}{4}y-\frac{1}{4}\left(-4\right)=\frac{1}{6}$$

Express -\frac{1}{4}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$\frac{1}{3}y-1-\frac{1}{4}y+\frac{4}{4}=\frac{1}{6}$$

Divide 4 by 4 to get 1.

$$\frac{1}{3}y-1-\frac{1}{4}y+1=\frac{1}{6}$$

Combine \frac{1}{3}y and -\frac{1}{4}y to get \frac{1}{12}y.

$$\frac{1}{12}y-1+1=\frac{1}{6}$$

Add -1 and 1 to get 0.

$$\frac{1}{12}y=\frac{1}{6}$$

Multiply both sides by 12, the reciprocal of \frac{1}{12}.

$$y=\frac{1}{6}\times 12$$

Multiply \frac{1}{6} and 12 to get \frac{12}{6}.

$$y=\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$y=2$$