Solve -1/3{6(p+q)-3[p-2(p-3q)]}

$$- \frac { 1 } { 3 } \{ 6 ( p + q ) - 3 [ p - 2 ( p - 3 q ) ] \}$$

Evaluate

$$4q-3p$$

Solution Steps

Use the distributive property to multiply 6 by p+q.

$$-\frac{1}{3}\left(6p+6q-3\left(p-2\left(p-3q\right)\right)\right)$$

Use the distributive property to multiply -2 by p-3q.

$$-\frac{1}{3}\left(6p+6q-3\left(p-2p+6q\right)\right)$$

Combine p and -2p to get -p.

$$-\frac{1}{3}\left(6p+6q-3\left(-p+6q\right)\right)$$

Use the distributive property to multiply -3 by -p+6q.

$$-\frac{1}{3}\left(6p+6q+3p-18q\right)$$

Combine 6p and 3p to get 9p.

$$-\frac{1}{3}\left(9p+6q-18q\right)$$

Combine 6q and -18q to get -12q.

$$-\frac{1}{3}\left(9p-12q\right)$$

Use the distributive property to multiply -\frac{1}{3} by 9p-12q.

$$-\frac{1}{3}\times 9p-\frac{1}{3}\left(-12\right)q$$

Express -\frac{1}{3}\times 9 as a single fraction.

$$\frac{-9}{3}p-\frac{1}{3}\left(-12\right)q$$

Divide -9 by 3 to get -3.

$$-3p-\frac{1}{3}\left(-12\right)q$$

Express -\frac{1}{3}\left(-12\right) as a single fraction.

$$-3p+\frac{-\left(-12\right)}{3}q$$

Multiply -1 and -12 to get 12.

$$-3p+\frac{12}{3}q$$

Divide 12 by 3 to get 4.

$$-3p+4q$$

Expand

$$4q-3p$$

Solution Steps

Use the distributive property to multiply 6 by p+q.

$$-\frac{1}{3}\left(6p+6q-3\left(p-2\left(p-3q\right)\right)\right)$$

Use the distributive property to multiply -2 by p-3q.

$$-\frac{1}{3}\left(6p+6q-3\left(p-2p+6q\right)\right)$$

Combine p and -2p to get -p.

$$-\frac{1}{3}\left(6p+6q-3\left(-p+6q\right)\right)$$

Use the distributive property to multiply -3 by -p+6q.

$$-\frac{1}{3}\left(6p+6q+3p-18q\right)$$

Combine 6p and 3p to get 9p.

$$-\frac{1}{3}\left(9p+6q-18q\right)$$

Combine 6q and -18q to get -12q.

$$-\frac{1}{3}\left(9p-12q\right)$$

Use the distributive property to multiply -\frac{1}{3} by 9p-12q.

$$-\frac{1}{3}\times 9p-\frac{1}{3}\left(-12\right)q$$

Express -\frac{1}{3}\times 9 as a single fraction.

$$\frac{-9}{3}p-\frac{1}{3}\left(-12\right)q$$

Divide -9 by 3 to get -3.

$$-3p-\frac{1}{3}\left(-12\right)q$$

Express -\frac{1}{3}\left(-12\right) as a single fraction.

$$-3p+\frac{-\left(-12\right)}{3}q$$

Multiply -1 and -12 to get 12.

$$-3p+\frac{12}{3}q$$

Divide 12 by 3 to get 4.

$$-3p+4q$$