Solve 1/2(12p-4)+1/3(2-6p)

$$\frac { 1 } { 2 } ( 12 p - 4 ) + \frac { 1 } { 3 } ( 2 - 6 p )$$

Evaluate

$$4p-\frac{4}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 12p-4.

$$\frac{1}{2}\times 12p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Multiply \frac{1}{2} and 12 to get \frac{12}{2}.

$$\frac{12}{2}p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Divide 12 by 2 to get 6.

$$6p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$6p+\frac{-4}{2}+\frac{1}{3}\left(2-6p\right)$$

Divide -4 by 2 to get -2.

$$6p-2+\frac{1}{3}\left(2-6p\right)$$

Use the distributive property to multiply \frac{1}{3} by 2-6p.

$$6p-2+\frac{1}{3}\times 2+\frac{1}{3}\left(-6\right)p$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$6p-2+\frac{2}{3}+\frac{1}{3}\left(-6\right)p$$

Multiply \frac{1}{3} and -6 to get \frac{-6}{3}.

$$6p-2+\frac{2}{3}+\frac{-6}{3}p$$

Divide -6 by 3 to get -2.

$$6p-2+\frac{2}{3}-2p$$

Convert -2 to fraction -\frac{6}{3}.

$$6p-\frac{6}{3}+\frac{2}{3}-2p$$

Since -\frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$6p+\frac{-6+2}{3}-2p$$

Add -6 and 2 to get -4.

$$6p-\frac{4}{3}-2p$$

Combine 6p and -2p to get 4p.

$$4p-\frac{4}{3}$$

Expand

$$4p-\frac{4}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 12p-4.

$$\frac{1}{2}\times 12p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Multiply \frac{1}{2} and 12 to get \frac{12}{2}.

$$\frac{12}{2}p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Divide 12 by 2 to get 6.

$$6p+\frac{1}{2}\left(-4\right)+\frac{1}{3}\left(2-6p\right)$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$6p+\frac{-4}{2}+\frac{1}{3}\left(2-6p\right)$$

Divide -4 by 2 to get -2.

$$6p-2+\frac{1}{3}\left(2-6p\right)$$

Use the distributive property to multiply \frac{1}{3} by 2-6p.

$$6p-2+\frac{1}{3}\times 2+\frac{1}{3}\left(-6\right)p$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$6p-2+\frac{2}{3}+\frac{1}{3}\left(-6\right)p$$

Multiply \frac{1}{3} and -6 to get \frac{-6}{3}.

$$6p-2+\frac{2}{3}+\frac{-6}{3}p$$

Divide -6 by 3 to get -2.

$$6p-2+\frac{2}{3}-2p$$

Convert -2 to fraction -\frac{6}{3}.

$$6p-\frac{6}{3}+\frac{2}{3}-2p$$

Since -\frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$6p+\frac{-6+2}{3}-2p$$

Add -6 and 2 to get -4.

$$6p-\frac{4}{3}-2p$$

Combine 6p and -2p to get 4p.

$$4p-\frac{4}{3}$$