Solve y+1/2+3y-6/3-8-y/6=1

$$\frac { y + 1 } { 2 } + \frac { 3 y - 6 } { 3 } - \frac { 8 - y } { 6 } = 1$$

Solve for y

$$y = \frac{23}{10} = 2\frac{3}{10} = 2.3$$

Steps for Solving Linear Equation

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

$$3\left(y+1\right)+2\left(3y-6\right)-\left(8-y\right)=6$$

Use the distributive property to multiply 3 by y+1.

$$3y+3+2\left(3y-6\right)-\left(8-y\right)=6$$

Use the distributive property to multiply 2 by 3y-6.

$$3y+3+6y-12-\left(8-y\right)=6$$

Combine 3y and 6y to get 9y.

$$9y+3-12-\left(8-y\right)=6$$

Subtract 12 from 3 to get -9.

$$9y-9-\left(8-y\right)=6$$

To find the opposite of 8-y, find the opposite of each term.

$$9y-9-8-\left(-y\right)=6$$

The opposite of -y is y.

$$9y-9-8+y=6$$

Subtract 8 from -9 to get -17.

$$9y-17+y=6$$

Combine 9y and y to get 10y.

$$10y-17=6$$

Add 17 to both sides.

$$10y=6+17$$

Add 6 and 17 to get 23.

$$10y=23$$

Divide both sides by 10.

$$y=\frac{23}{10}$$