Solve 2n-3{2(5n-4)-4[n-(7n-y)]}

$$2 n - 3 \{ 2 ( 5 n - 4 ) - 4 [ n - ( 7 n - y ) ] \}$$

Evaluate

$$12y-100n+24$$

Solution Steps

Use the distributive property to multiply 2 by 5n-4.

$$2n-3\left(10n-8-4\left(n-\left(7n-y\right)\right)\right)$$

To find the opposite of 7n-y, find the opposite of each term.

$$2n-3\left(10n-8-4\left(n-7n-\left(-y\right)\right)\right)$$

The opposite of -y is y.

$$2n-3\left(10n-8-4\left(n-7n+y\right)\right)$$

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

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

Use the distributive property to multiply -4 by -6n+y.

$$2n-3\left(10n-8+24n-4y\right)$$

Combine 10n and 24n to get 34n.

$$2n-3\left(34n-8-4y\right)$$

Use the distributive property to multiply -3 by 34n-8-4y.

$$2n-102n+24+12y$$

Combine 2n and -102n to get -100n.

$$-100n+24+12y$$

Expand

$$12y-100n+24$$

Solution Steps

Use the distributive property to multiply 2 by 5n-4.

$$2n-3\left(10n-8-4\left(n-\left(7n-y\right)\right)\right)$$

To find the opposite of 7n-y, find the opposite of each term.

$$2n-3\left(10n-8-4\left(n-7n-\left(-y\right)\right)\right)$$

The opposite of -y is y.

$$2n-3\left(10n-8-4\left(n-7n+y\right)\right)$$

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

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

Use the distributive property to multiply -4 by -6n+y.

$$2n-3\left(10n-8+24n-4y\right)$$

Combine 10n and 24n to get 34n.

$$2n-3\left(34n-8-4y\right)$$

Use the distributive property to multiply -3 by 34n-8-4y.

$$2n-102n+24+12y$$

Combine 2n and -102n to get -100n.

$$-100n+24+12y$$