Solve 3x+7y+5left(6-x-yright)+2(4-x)+3(7-y)+9(3-(6-x-y))

$$3x+7y+5 \left( 6-x-y \right) +2(4-x)+3(7-y)+9(3-(6-x-y))$$

Evaluate

$$5x+8y+32$$

Solution Steps

Use the distributive property to multiply 5 by 6-x-y.

$$3x+7y+30-5x-5y+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

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

$$-2x+7y+30-5y+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Combine 7y and -5y to get 2y.

$$-2x+2y+30+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Use the distributive property to multiply 2 by 4-x.

$$-2x+2y+30+8-2x+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Add 30 and 8 to get 38.

$$-2x+2y+38-2x+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

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

$$-4x+2y+38+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Use the distributive property to multiply 3 by 7-y.

$$-4x+2y+38+21-3y+9\left(3-\left(6-x-y\right)\right)$$

Add 38 and 21 to get 59.

$$-4x+2y+59-3y+9\left(3-\left(6-x-y\right)\right)$$

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

$$-4x-y+59+9\left(3-\left(6-x-y\right)\right)$$

To find the opposite of 6-x-y, find the opposite of each term.

$$-4x-y+59+9\left(3-6-\left(-x\right)-\left(-y\right)\right)$$

The opposite of -x is x.

$$-4x-y+59+9\left(3-6+x-\left(-y\right)\right)$$

The opposite of -y is y.

$$-4x-y+59+9\left(3-6+x+y\right)$$

Subtract 6 from 3 to get -3.

$$-4x-y+59+9\left(-3+x+y\right)$$

Use the distributive property to multiply 9 by -3+x+y.

$$-4x-y+59-27+9x+9y$$

Subtract 27 from 59 to get 32.

$$-4x-y+32+9x+9y$$

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

$$5x-y+32+9y$$

Combine -y and 9y to get 8y.

$$5x+8y+32$$

Expand

$$5x+8y+32$$

Solution Steps

Use the distributive property to multiply 5 by 6-x-y.

$$3x+7y+30-5x-5y+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

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

$$-2x+7y+30-5y+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Combine 7y and -5y to get 2y.

$$-2x+2y+30+2\left(4-x\right)+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Use the distributive property to multiply 2 by 4-x.

$$-2x+2y+30+8-2x+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Add 30 and 8 to get 38.

$$-2x+2y+38-2x+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

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

$$-4x+2y+38+3\left(7-y\right)+9\left(3-\left(6-x-y\right)\right)$$

Use the distributive property to multiply 3 by 7-y.

$$-4x+2y+38+21-3y+9\left(3-\left(6-x-y\right)\right)$$

Add 38 and 21 to get 59.

$$-4x+2y+59-3y+9\left(3-\left(6-x-y\right)\right)$$

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

$$-4x-y+59+9\left(3-\left(6-x-y\right)\right)$$

To find the opposite of 6-x-y, find the opposite of each term.

$$-4x-y+59+9\left(3-6-\left(-x\right)-\left(-y\right)\right)$$

The opposite of -x is x.

$$-4x-y+59+9\left(3-6+x-\left(-y\right)\right)$$

The opposite of -y is y.

$$-4x-y+59+9\left(3-6+x+y\right)$$

Subtract 6 from 3 to get -3.

$$-4x-y+59+9\left(-3+x+y\right)$$

Use the distributive property to multiply 9 by -3+x+y.

$$-4x-y+59-27+9x+9y$$

Subtract 27 from 59 to get 32.

$$-4x-y+32+9x+9y$$

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

$$5x-y+32+9y$$

Combine -y and 9y to get 8y.

$$5x+8y+32$$