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

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

Solve for y

$$y = \frac{47}{9} = 5\frac{2}{9} \approx 5.222222222$$

Steps for Solving Linear Equation

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

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply 3 and 3 to get 9.

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

Multiply 4 and 3 to get 12.

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

Add 12 and 2 to get 14.

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

Multiply -2 and 14 to get -28.

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

Multiply 4 and 6 to get 24.

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

Add 24 and 5 to get 29.

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

Add 3 and 2 to get 5.

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

Multiply -2 and 5 to get -10.

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

Subtract 10 from 29 to get 19.

$$9y-28=19$$

Add 28 to both sides.

$$9y=19+28$$

Add 19 and 28 to get 47.

$$9y=47$$

Divide both sides by 9.

$$y=\frac{47}{9}$$