Solve 2/5[12p-(5+2p)]

$$\frac { 2 } { 5 } [ 12 p - ( 5 + 2 p ) ]$$

Evaluate

$$4p-2$$

Solution Steps

To find the opposite of 5+2p, find the opposite of each term.

$$\frac{2}{5}\left(12p-5-2p\right)$$

Combine 12p and -2p to get 10p.

$$\frac{2}{5}\left(10p-5\right)$$

Use the distributive property to multiply \frac{2}{5} by 10p-5.

$$\frac{2}{5}\times 10p+\frac{2}{5}\left(-5\right)$$

Express \frac{2}{5}\times 10 as a single fraction.

$$\frac{2\times 10}{5}p+\frac{2}{5}\left(-5\right)$$

Multiply 2 and 10 to get 20.

$$\frac{20}{5}p+\frac{2}{5}\left(-5\right)$$

Divide 20 by 5 to get 4.

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

Express \frac{2}{5}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

$$4p+\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$4p-2$$

Expand

$$4p-2$$

Solution Steps

To find the opposite of 5+2p, find the opposite of each term.

$$\frac{2}{5}\left(12p-5-2p\right)$$

Combine 12p and -2p to get 10p.

$$\frac{2}{5}\left(10p-5\right)$$

Use the distributive property to multiply \frac{2}{5} by 10p-5.

$$\frac{2}{5}\times 10p+\frac{2}{5}\left(-5\right)$$

Express \frac{2}{5}\times 10 as a single fraction.

$$\frac{2\times 10}{5}p+\frac{2}{5}\left(-5\right)$$

Multiply 2 and 10 to get 20.

$$\frac{20}{5}p+\frac{2}{5}\left(-5\right)$$

Divide 20 by 5 to get 4.

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

Express \frac{2}{5}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

$$4p+\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$4p-2$$