Solve m-(m+n)-3{-2m+[-2m+n+2(-1+n)-(m+n-1)]}

$$m - ( m + n ) - 3 \{ - 2 m + [ - 2 m + n + 2 ( - 1 + n ) - ( m + n - 1 ) ] \}$$

Evaluate

$$15m-7n+3$$

Solution Steps

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

$$m-m-n-3\left(-2m-2m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Combine m and -m to get 0.

$$-n-3\left(-2m-2m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Combine -2m and -2m to get -4m.

$$-n-3\left(-4m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Use the distributive property to multiply 2 by -1+n.

$$-n-3\left(-4m+n-2+2n-\left(m+n-1\right)\right)$$

Combine n and 2n to get 3n.

$$-n-3\left(-4m+3n-2-\left(m+n-1\right)\right)$$

To find the opposite of m+n-1, find the opposite of each term.

$$-n-3\left(-4m+3n-2-m-n-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$-n-3\left(-4m+3n-2-m-n+1\right)$$

Combine -4m and -m to get -5m.

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

Combine 3n and -n to get 2n.

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

Add -2 and 1 to get -1.

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

Use the distributive property to multiply -3 by -5m+2n-1.

$$-n+15m-6n+3$$

Combine -n and -6n to get -7n.

$$-7n+15m+3$$

Expand

$$15m-7n+3$$

Solution Steps

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

$$m-m-n-3\left(-2m-2m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Combine m and -m to get 0.

$$-n-3\left(-2m-2m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Combine -2m and -2m to get -4m.

$$-n-3\left(-4m+n+2\left(-1+n\right)-\left(m+n-1\right)\right)$$

Use the distributive property to multiply 2 by -1+n.

$$-n-3\left(-4m+n-2+2n-\left(m+n-1\right)\right)$$

Combine n and 2n to get 3n.

$$-n-3\left(-4m+3n-2-\left(m+n-1\right)\right)$$

To find the opposite of m+n-1, find the opposite of each term.

$$-n-3\left(-4m+3n-2-m-n-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$-n-3\left(-4m+3n-2-m-n+1\right)$$

Combine -4m and -m to get -5m.

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

Combine 3n and -n to get 2n.

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

Add -2 and 1 to get -1.

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

Use the distributive property to multiply -3 by -5m+2n-1.

$$-n+15m-6n+3$$

Combine -n and -6n to get -7n.

$$-7n+15m+3$$