Solve [3m-(6n+4)]-[(8m-7)+(2n-3)-(4m+5n)]

$$[ 3 m - ( 6 n + 4 ) ] - [ ( 8 m - 7 ) + ( 2 n - 3 ) - ( 4 m + 5 n ) ]$$

Evaluate

$$6-3n-m$$

Solution Steps

To find the opposite of 6n+4, find the opposite of each term.

$$3m-6n-4-\left(8m-7+2n-3-\left(4m+5n\right)\right)$$

Subtract 3 from -7 to get -10.

$$3m-6n-4-\left(8m-10+2n-\left(4m+5n\right)\right)$$

To find the opposite of 4m+5n, find the opposite of each term.

$$3m-6n-4-\left(8m-10+2n-4m-5n\right)$$

Combine 8m and -4m to get 4m.

$$3m-6n-4-\left(4m-10+2n-5n\right)$$

Combine 2n and -5n to get -3n.

$$3m-6n-4-\left(4m-10-3n\right)$$

To find the opposite of 4m-10-3n, find the opposite of each term.

$$3m-6n-4-4m-\left(-10\right)-\left(-3n\right)$$

The opposite of -10 is 10.

$$3m-6n-4-4m+10-\left(-3n\right)$$

The opposite of -3n is 3n.

$$3m-6n-4-4m+10+3n$$

Combine 3m and -4m to get -m.

$$-m-6n-4+10+3n$$

Add -4 and 10 to get 6.

$$-m-6n+6+3n$$

Combine -6n and 3n to get -3n.

$$-m-3n+6$$

Expand

$$6-3n-m$$

Solution Steps

To find the opposite of 6n+4, find the opposite of each term.

$$3m-6n-4-\left(8m-7+2n-3-\left(4m+5n\right)\right)$$

Subtract 3 from -7 to get -10.

$$3m-6n-4-\left(8m-10+2n-\left(4m+5n\right)\right)$$

To find the opposite of 4m+5n, find the opposite of each term.

$$3m-6n-4-\left(8m-10+2n-4m-5n\right)$$

Combine 8m and -4m to get 4m.

$$3m-6n-4-\left(4m-10+2n-5n\right)$$

Combine 2n and -5n to get -3n.

$$3m-6n-4-\left(4m-10-3n\right)$$

To find the opposite of 4m-10-3n, find the opposite of each term.

$$3m-6n-4-4m-\left(-10\right)-\left(-3n\right)$$

The opposite of -10 is 10.

$$3m-6n-4-4m+10-\left(-3n\right)$$

The opposite of -3n is 3n.

$$3m-6n-4-4m+10+3n$$

Combine 3m and -4m to get -m.

$$-m-6n-4+10+3n$$

Add -4 and 10 to get 6.

$$-m-6n+6+3n$$

Combine -6n and 3n to get -3n.

$$-m-3n+6$$