Solve -(3/4p+1/6q-r)+(-1/2p-1/3q)-(frac{1}{4}p-2r)=

$$- ( \frac { 3 } { 4 } p + \frac { 1 } { 6 } q - r ) + ( - \frac { 1 } { 2 } p - \frac { 1 } { 3 } q ) - ( \frac { 1 } { 4 } p - 2 r ) =$$

Evaluate

$$-\frac{q}{2}-\frac{3p}{2}+3r$$

Solution Steps

To find the opposite of \frac{3}{4}p+\frac{1}{6}q-r, find the opposite of each term.

$$-\frac{3}{4}p-\frac{1}{6}q-\left(-r\right)-\frac{1}{2}p-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

The opposite of -r is r.

$$-\frac{3}{4}p-\frac{1}{6}q+r-\frac{1}{2}p-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

Combine -\frac{3}{4}p and -\frac{1}{2}p to get -\frac{5}{4}p.

$$-\frac{5}{4}p-\frac{1}{6}q+r-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

Combine -\frac{1}{6}q and -\frac{1}{3}q to get -\frac{1}{2}q.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\left(\frac{1}{4}p-2r\right)$$

To find the opposite of \frac{1}{4}p-2r, find the opposite of each term.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\frac{1}{4}p-\left(-2r\right)$$

The opposite of -2r is 2r.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\frac{1}{4}p+2r$$

Combine -\frac{5}{4}p and -\frac{1}{4}p to get -\frac{3}{2}p.

$$-\frac{3}{2}p-\frac{1}{2}q+r+2r$$

Combine r and 2r to get 3r.

$$-\frac{3}{2}p-\frac{1}{2}q+3r$$

Expand

$$-\frac{q}{2}-\frac{3p}{2}+3r$$

Solution Steps

To find the opposite of \frac{3}{4}p+\frac{1}{6}q-r, find the opposite of each term.

$$-\frac{3}{4}p-\frac{1}{6}q-\left(-r\right)-\frac{1}{2}p-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

The opposite of -r is r.

$$-\frac{3}{4}p-\frac{1}{6}q+r-\frac{1}{2}p-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

Combine -\frac{3}{4}p and -\frac{1}{2}p to get -\frac{5}{4}p.

$$-\frac{5}{4}p-\frac{1}{6}q+r-\frac{1}{3}q-\left(\frac{1}{4}p-2r\right)$$

Combine -\frac{1}{6}q and -\frac{1}{3}q to get -\frac{1}{2}q.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\left(\frac{1}{4}p-2r\right)$$

To find the opposite of \frac{1}{4}p-2r, find the opposite of each term.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\frac{1}{4}p-\left(-2r\right)$$

The opposite of -2r is 2r.

$$-\frac{5}{4}p-\frac{1}{2}q+r-\frac{1}{4}p+2r$$

Combine -\frac{5}{4}p and -\frac{1}{4}p to get -\frac{3}{2}p.

$$-\frac{3}{2}p-\frac{1}{2}q+r+2r$$

Combine r and 2r to get 3r.

$$-\frac{3}{2}p-\frac{1}{2}q+3r$$