Solve [-2(3a+b)-(4x+3y)+9]-[9(a-b)-2(x+y)+11]

$$[ - 2 ( 3 a + b ) - ( 4 x + 3 y ) + 9 ] - [ 9 ( a - b ) - 2 ( x + y ) + 11 ]$$

Evaluate

$$-2x-y+7b-15a-2$$

Solution Steps

Use the distributive property to multiply -2 by 3a+b.

$$-6a-2b-\left(4x+3y\right)+9-\left(9\left(a-b\right)-2\left(x+y\right)+11\right)$$

To find the opposite of 4x+3y, find the opposite of each term.

$$-6a-2b-4x-3y+9-\left(9\left(a-b\right)-2\left(x+y\right)+11\right)$$

Use the distributive property to multiply 9 by a-b.

$$-6a-2b-4x-3y+9-\left(9a-9b-2\left(x+y\right)+11\right)$$

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

$$-6a-2b-4x-3y+9-\left(9a-9b-2x-2y+11\right)$$

To find the opposite of 9a-9b-2x-2y+11, find the opposite of each term.

$$-6a-2b-4x-3y+9-9a-\left(-9b\right)-\left(-2x\right)-\left(-2y\right)-11$$

Combine -6a and -9a to get -15a.

$$-15a-2b-4x-3y+9-\left(-9b\right)-\left(-2x\right)-\left(-2y\right)-11$$

The opposite of -9b is 9b.

$$-15a-2b-4x-3y+9+9b-\left(-2x\right)-\left(-2y\right)-11$$

Combine -2b and 9b to get 7b.

$$-15a+7b-4x-3y+9-\left(-2x\right)-\left(-2y\right)-11$$

The opposite of -2x is 2x.

$$-15a+7b-4x-3y+9+2x-\left(-2y\right)-11$$

Combine -4x and 2x to get -2x.

$$-15a+7b-2x-3y+9-\left(-2y\right)-11$$

The opposite of -2y is 2y.

$$-15a+7b-2x-3y+9+2y-11$$

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

$$-15a+7b-2x-y+9-11$$

Subtract 11 from 9 to get -2.

$$-15a+7b-2x-y-2$$

Expand

$$-2x-y+7b-15a-2$$

Solution Steps

Use the distributive property to multiply -2 by 3a+b.

$$-6a-2b-\left(4x+3y\right)+9-\left(9\left(a-b\right)-2\left(x+y\right)+11\right)$$

To find the opposite of 4x+3y, find the opposite of each term.

$$-6a-2b-4x-3y+9-\left(9\left(a-b\right)-2\left(x+y\right)+11\right)$$

Use the distributive property to multiply 9 by a-b.

$$-6a-2b-4x-3y+9-\left(9a-9b-2\left(x+y\right)+11\right)$$

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

$$-6a-2b-4x-3y+9-\left(9a-9b-2x-2y+11\right)$$

To find the opposite of 9a-9b-2x-2y+11, find the opposite of each term.

$$-6a-2b-4x-3y+9-9a-\left(-9b\right)-\left(-2x\right)-\left(-2y\right)-11$$

Combine -6a and -9a to get -15a.

$$-15a-2b-4x-3y+9-\left(-9b\right)-\left(-2x\right)-\left(-2y\right)-11$$

The opposite of -9b is 9b.

$$-15a-2b-4x-3y+9+9b-\left(-2x\right)-\left(-2y\right)-11$$

Combine -2b and 9b to get 7b.

$$-15a+7b-4x-3y+9-\left(-2x\right)-\left(-2y\right)-11$$

The opposite of -2x is 2x.

$$-15a+7b-4x-3y+9+2x-\left(-2y\right)-11$$

Combine -4x and 2x to get -2x.

$$-15a+7b-2x-3y+9-\left(-2y\right)-11$$

The opposite of -2y is 2y.

$$-15a+7b-2x-3y+9+2y-11$$

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

$$-15a+7b-2x-y+9-11$$

Subtract 11 from 9 to get -2.

$$-15a+7b-2x-y-2$$