Solve 5(y-1/5)-2(6+y)=3(4y-5)+y

$$5 ( y - 1 / 5 ) - 2 ( 6 + y ) = 3 ( 4 y - 5 ) + y$$

Solve for y

$$y=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by y-\frac{1}{5}.

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

Cancel out 5 and 5.

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

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

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

Subtract 12 from -1 to get -13.

$$5y-13-2y=3\left(4y-5\right)+y$$

Combine 5y and -2y to get 3y.

$$3y-13=3\left(4y-5\right)+y$$

Use the distributive property to multiply 3 by 4y-5.

$$3y-13=12y-15+y$$

Combine 12y and y to get 13y.

$$3y-13=13y-15$$

Subtract 13y from both sides.

$$3y-13-13y=-15$$

Combine 3y and -13y to get -10y.

$$-10y-13=-15$$

Add 13 to both sides.

$$-10y=-15+13$$

Add -15 and 13 to get -2.

$$-10y=-2$$

Divide both sides by -10.

$$y=\frac{-2}{-10}$$

Reduce the fraction \frac{-2}{-10} to lowest terms by extracting and canceling out -2.

$$y=\frac{1}{5}$$