Solve (1,5m+2,3n+5p)-(-2,3m-3,2p+12n

$$( 1,5 m + 2,3 n + 5 p ) - ( - 2,3 m - 3,2 p + 12 n$$

Evaluate

$$\frac{19m}{5}+\frac{41p}{5}-\frac{97n}{10}$$

Solution Steps

To find the opposite of -2,3m-3,2p+12n, find the opposite of each term.

$$1,5m+2,3n+5p-\left(-2,3m\right)-\left(-3,2p\right)-12n$$

The opposite of -2,3m is 2,3m.

$$1,5m+2,3n+5p+2,3m-\left(-3,2p\right)-12n$$

The opposite of -3,2p is 3,2p.

$$1,5m+2,3n+5p+2,3m+3,2p-12n$$

Combine 1,5m and 2,3m to get 3,8m.

$$3,8m+2,3n+5p+3,2p-12n$$

Combine 5p and 3,2p to get 8,2p.

$$3,8m+2,3n+8,2p-12n$$

Combine 2,3n and -12n to get -9,7n.

$$3,8m-9,7n+8,2p$$

Expand

$$\frac{19m}{5}+\frac{41p}{5}-\frac{97n}{10}$$

Solution Steps

To find the opposite of -2,3m-3,2p+12n, find the opposite of each term.

$$1,5m+2,3n+5p-\left(-2,3m\right)-\left(-3,2p\right)-12n$$

The opposite of -2,3m is 2,3m.

$$1,5m+2,3n+5p+2,3m-\left(-3,2p\right)-12n$$

The opposite of -3,2p is 3,2p.

$$1,5m+2,3n+5p+2,3m+3,2p-12n$$

Combine 1,5m and 2,3m to get 3,8m.

$$3,8m+2,3n+5p+3,2p-12n$$

Combine 5p and 3,2p to get 8,2p.

$$3,8m+2,3n+8,2p-12n$$

Combine 2,3n and -12n to get -9,7n.

$$3,8m-9,7n+8,2p$$