Solve for y 5y-2+y-6=-9y+10+6y+13

$5 y - 2 + y - 6 = - 9 y + 10 + 6 y + 13$

Simplify $5 y - 2 + y - 6$ .

Add $5 y$ and $y$ .

$6 y - 2 - 6 = - 9 y + 10 + 6 y + 13$

Subtract $6$ from $- 2$ .

$6 y - 8 = - 9 y + 10 + 6 y + 13$

Simplify $- 9 y + 10 + 6 y + 13$ .

Add $- 9 y$ and $6 y$ .

$6 y - 8 = - 3 y + 10 + 13$

Add $10$ and $13$ .

$6 y - 8 = - 3 y + 23$

Move all terms containing $y$ to the left side of the equation.

Add $3 y$ to both sides of the equation.

$6 y - 8 + 3 y = 23$

Add $6 y$ and $3 y$ .

$9 y - 8 = 23$

Move all terms not containing $y$ to the right side of the equation.

Add $8$ to both sides of the equation.

$9 y = 23 + 8$

Add $23$ and $8$ .

$9 y = 31$

Divide each term in $9 y = 31$ by $9$ and simplify.

Divide each term in $9 y = 31$ by $9$ .

$\frac{9 y}{9} = \frac{31}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{31}{9}$

Divide $y$ by $1$ .

$y = \frac{31}{9}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{31}{9}$

Decimal Form:

$y = 3.\overline{4}$

Mixed Number Form:

$y = 3 \frac{4}{9}$