Solve [2p-(5t+q)+(-9p-3t)+(8q+6t)+t-3p-5q]=

$$[ 2 p - ( 5 t + q ) + ( - 9 p - 3 t ) + ( 8 q + 6 t ) + t - 3 p - 5 q ] =$$

Evaluate

$$-10p+2q-t$$

Solution Steps

To find the opposite of 5t+q, find the opposite of each term.

$$2p-5t-q-9p-3t+8q+6t+t-3p-5q$$

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

$$-7p-5t-q-3t+8q+6t+t-3p-5q$$

Combine -5t and -3t to get -8t.

$$-7p-8t-q+8q+6t+t-3p-5q$$

Combine -q and 8q to get 7q.

$$-7p-8t+7q+6t+t-3p-5q$$

Combine -8t and 6t to get -2t.

$$-7p-2t+7q+t-3p-5q$$

Combine -2t and t to get -t.

$$-7p-t+7q-3p-5q$$

Combine -7p and -3p to get -10p.

$$-10p-t+7q-5q$$

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

$$-10p-t+2q$$

Expand

$$-10p+2q-t$$

Solution Steps

To find the opposite of 5t+q, find the opposite of each term.

$$2p-5t-q-9p-3t+8q+6t+t-3p-5q$$

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

$$-7p-5t-q-3t+8q+6t+t-3p-5q$$

Combine -5t and -3t to get -8t.

$$-7p-8t-q+8q+6t+t-3p-5q$$

Combine -q and 8q to get 7q.

$$-7p-8t+7q+6t+t-3p-5q$$

Combine -8t and 6t to get -2t.

$$-7p-2t+7q+t-3p-5q$$

Combine -2t and t to get -t.

$$-7p-t+7q-3p-5q$$

Combine -7p and -3p to get -10p.

$$-10p-t+7q-5q$$

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

$$-10p-t+2q$$