Solve 1/3(2y+7)-1/9(1-4)=

$$\frac { 1 } { 3 } ( 2 y + 7 ) - \frac { 1 } { 9 } ( 1 - 4 ) =$$

Evaluate

$$\frac{2\left(y+4\right)}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 2y+7.

$$\frac{1}{3}\times 2y+\frac{1}{3}\times 7-\frac{1}{9}\left(1-4\right)$$

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

$$\frac{2}{3}y+\frac{1}{3}\times 7-\frac{1}{9}\left(1-4\right)$$

Multiply \frac{1}{3} and 7 to get \frac{7}{3}.

$$\frac{2}{3}y+\frac{7}{3}-\frac{1}{9}\left(1-4\right)$$

Subtract 4 from 1 to get -3.

$$\frac{2}{3}y+\frac{7}{3}-\frac{1}{9}\left(-3\right)$$

Multiply \frac{1}{9} and -3 to get \frac{-3}{9}.

$$\frac{2}{3}y+\frac{7}{3}-\frac{-3}{9}$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}y+\frac{7}{3}-\left(-\frac{1}{3}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{2}{3}y+\frac{7}{3}+\frac{1}{3}$$

Since \frac{7}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}y+\frac{7+1}{3}$$

Add 7 and 1 to get 8.

$$\frac{2}{3}y+\frac{8}{3}$$

Expand

$$\frac{2y+8}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 2y+7.

$$\frac{1}{3}\times 2y+\frac{1}{3}\times 7-\frac{1}{9}\left(1-4\right)$$

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

$$\frac{2}{3}y+\frac{1}{3}\times 7-\frac{1}{9}\left(1-4\right)$$

Multiply \frac{1}{3} and 7 to get \frac{7}{3}.

$$\frac{2}{3}y+\frac{7}{3}-\frac{1}{9}\left(1-4\right)$$

Subtract 4 from 1 to get -3.

$$\frac{2}{3}y+\frac{7}{3}-\frac{1}{9}\left(-3\right)$$

Multiply \frac{1}{9} and -3 to get \frac{-3}{9}.

$$\frac{2}{3}y+\frac{7}{3}-\frac{-3}{9}$$

Reduce the fraction \frac{-3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}y+\frac{7}{3}-\left(-\frac{1}{3}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{2}{3}y+\frac{7}{3}+\frac{1}{3}$$

Since \frac{7}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}y+\frac{7+1}{3}$$

Add 7 and 1 to get 8.

$$\frac{2}{3}y+\frac{8}{3}$$