Solve (7a-4b+3c-18)-(8a+7b-8c+6)+5(2a-b+2c-3)=

$$( 7 a - 4 b + 3 c - 18 ) - ( 8 a + 7 b - 8 c + 6 ) + 5 ( 2 a - b + 2 c - 3 ) =$$

Evaluate

$$9a-16b+21c-39$$

Solution Steps

To find the opposite of 8a+7b-8c+6, find the opposite of each term.

$$7a-4b+3c-18-8a-7b-\left(-8c\right)-6+5\left(2a-b+2c-3\right)$$

The opposite of -8c is 8c.

$$7a-4b+3c-18-8a-7b+8c-6+5\left(2a-b+2c-3\right)$$

Combine 7a and -8a to get -a.

$$-a-4b+3c-18-7b+8c-6+5\left(2a-b+2c-3\right)$$

Combine -4b and -7b to get -11b.

$$-a-11b+3c-18+8c-6+5\left(2a-b+2c-3\right)$$

Combine 3c and 8c to get 11c.

$$-a-11b+11c-18-6+5\left(2a-b+2c-3\right)$$

Subtract 6 from -18 to get -24.

$$-a-11b+11c-24+5\left(2a-b+2c-3\right)$$

Use the distributive property to multiply 5 by 2a-b+2c-3.

$$-a-11b+11c-24+10a-5b+10c-15$$

Combine -a and 10a to get 9a.

$$9a-11b+11c-24-5b+10c-15$$

Combine -11b and -5b to get -16b.

$$9a-16b+11c-24+10c-15$$

Combine 11c and 10c to get 21c.

$$9a-16b+21c-24-15$$

Subtract 15 from -24 to get -39.

$$9a-16b+21c-39$$

Expand

$$9a-16b+21c-39$$

Solution Steps

To find the opposite of 8a+7b-8c+6, find the opposite of each term.

$$7a-4b+3c-18-8a-7b-\left(-8c\right)-6+5\left(2a-b+2c-3\right)$$

The opposite of -8c is 8c.

$$7a-4b+3c-18-8a-7b+8c-6+5\left(2a-b+2c-3\right)$$

Combine 7a and -8a to get -a.

$$-a-4b+3c-18-7b+8c-6+5\left(2a-b+2c-3\right)$$

Combine -4b and -7b to get -11b.

$$-a-11b+3c-18+8c-6+5\left(2a-b+2c-3\right)$$

Combine 3c and 8c to get 11c.

$$-a-11b+11c-18-6+5\left(2a-b+2c-3\right)$$

Subtract 6 from -18 to get -24.

$$-a-11b+11c-24+5\left(2a-b+2c-3\right)$$

Use the distributive property to multiply 5 by 2a-b+2c-3.

$$-a-11b+11c-24+10a-5b+10c-15$$

Combine -a and 10a to get 9a.

$$9a-11b+11c-24-5b+10c-15$$

Combine -11b and -5b to get -16b.

$$9a-16b+11c-24+10c-15$$

Combine 11c and 10c to get 21c.

$$9a-16b+21c-24-15$$

Subtract 15 from -24 to get -39.

$$9a-16b+21c-39$$