Solve 26-[4+6y-2(y+2)]=-2(5y-5)-[8(y-1)-9y+7]

$$26 - [ 4 + 6 y - 2 ( y + 2 ) ] = - 2 ( 5 y - 5 ) - [ 8 ( y - 1 ) - 9 y + 7 ]$$

Solve for y

$$y=-3$$

Steps for Solving Linear Equation

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

$$26-\left(4+6y-2y-4\right)=-2\left(5y-5\right)-\left(8\left(y-1\right)-9y+7\right)$$

Combine 6y and -2y to get 4y.

$$26-\left(4+4y-4\right)=-2\left(5y-5\right)-\left(8\left(y-1\right)-9y+7\right)$$

Subtract 4 from 4 to get 0.

$$26-4y=-2\left(5y-5\right)-\left(8\left(y-1\right)-9y+7\right)$$

Use the distributive property to multiply -2 by 5y-5.

$$26-4y=-10y+10-\left(8\left(y-1\right)-9y+7\right)$$

Use the distributive property to multiply 8 by y-1.

$$26-4y=-10y+10-\left(8y-8-9y+7\right)$$

Combine 8y and -9y to get -y.

$$26-4y=-10y+10-\left(-y-8+7\right)$$

Add -8 and 7 to get -1.

$$26-4y=-10y+10-\left(-y-1\right)$$

To find the opposite of -y-1, find the opposite of each term.

$$26-4y=-10y+10-\left(-y\right)-\left(-1\right)$$

The opposite of -y is y.

$$26-4y=-10y+10+y-\left(-1\right)$$

The opposite of -1 is 1.

$$26-4y=-10y+10+y+1$$

Combine -10y and y to get -9y.

$$26-4y=-9y+10+1$$

Add 10 and 1 to get 11.

$$26-4y=-9y+11$$

Add 9y to both sides.

$$26-4y+9y=11$$

Combine -4y and 9y to get 5y.

$$26+5y=11$$

Subtract 26 from both sides.

$$5y=11-26$$

Subtract 26 from 11 to get -15.

$$5y=-15$$

Divide both sides by 5.

$$y=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$y=-3$$