Solve 11/2y-42/3=45/6-12/3y

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

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(1\times 2+1\right)y-2\left(4\times 3+2\right)=4\times 6+5-2\left(1\times 3+2\right)y$$

Multiply 1 and 2 to get 2.

$$3\left(2+1\right)y-2\left(4\times 3+2\right)=4\times 6+5-2\left(1\times 3+2\right)y$$

Add 2 and 1 to get 3.

$$3\times 3y-2\left(4\times 3+2\right)=4\times 6+5-2\left(1\times 3+2\right)y$$

Multiply 3 and 3 to get 9.

$$9y-2\left(4\times 3+2\right)=4\times 6+5-2\left(1\times 3+2\right)y$$

Multiply 4 and 3 to get 12.

$$9y-2\left(12+2\right)=4\times 6+5-2\left(1\times 3+2\right)y$$

Add 12 and 2 to get 14.

$$9y-2\times 14=4\times 6+5-2\left(1\times 3+2\right)y$$

Multiply -2 and 14 to get -28.

$$9y-28=4\times 6+5-2\left(1\times 3+2\right)y$$

Multiply 4 and 6 to get 24.

$$9y-28=24+5-2\left(1\times 3+2\right)y$$

Add 24 and 5 to get 29.

$$9y-28=29-2\left(1\times 3+2\right)y$$

Multiply 1 and 3 to get 3.

$$9y-28=29-2\left(3+2\right)y$$

Add 3 and 2 to get 5.

$$9y-28=29-2\times 5y$$

Multiply 2 and 5 to get 10.

$$9y-28=29-10y$$

Add 10y to both sides.

$$9y-28+10y=29$$

Combine 9y and 10y to get 19y.

$$19y-28=29$$

Add 28 to both sides.

$$19y=29+28$$

Add 29 and 28 to get 57.

$$19y=57$$

Divide both sides by 19.

$$y=\frac{57}{19}$$

Divide 57 by 19 to get 3.

$$y=3$$