Solve 1/7-3(3/7n-2/7)

$$\frac { 1 } { 7 } - 3 ( \frac { 3 } { 7 } n - \frac { 2 } { 7 } )$$

Evaluate

$$-\frac{9n}{7}+1$$

Solution Steps

Use the distributive property to multiply -3 by \frac{3}{7}n-\frac{2}{7}.

$$\frac{1}{7}-3\times \frac{3}{7}n-3\left(-\frac{2}{7}\right)$$

Express -3\times \frac{3}{7} as a single fraction.

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

Multiply -3 and 3 to get -9.

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

Fraction \frac{-9}{7} can be rewritten as -\frac{9}{7} by extracting the negative sign.

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

Express -3\left(-\frac{2}{7}\right) as a single fraction.

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

Multiply -3 and -2 to get 6.

$$\frac{1}{7}-\frac{9}{7}n+\frac{6}{7}$$

Since \frac{1}{7} and \frac{6}{7} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{7}-\frac{9}{7}n$$

Add 1 and 6 to get 7.

$$\frac{7}{7}-\frac{9}{7}n$$

Divide 7 by 7 to get 1.

$$1-\frac{9}{7}n$$

Expand

$$-\frac{9n}{7}+1$$

Solution Steps

Use the distributive property to multiply -3 by \frac{3}{7}n-\frac{2}{7}.

$$\frac{1}{7}-3\times \frac{3}{7}n-3\left(-\frac{2}{7}\right)$$

Express -3\times \frac{3}{7} as a single fraction.

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

Multiply -3 and 3 to get -9.

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

Fraction \frac{-9}{7} can be rewritten as -\frac{9}{7} by extracting the negative sign.

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

Express -3\left(-\frac{2}{7}\right) as a single fraction.

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

Multiply -3 and -2 to get 6.

$$\frac{1}{7}-\frac{9}{7}n+\frac{6}{7}$$

Since \frac{1}{7} and \frac{6}{7} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{7}-\frac{9}{7}n$$

Add 1 and 6 to get 7.

$$\frac{7}{7}-\frac{9}{7}n$$

Divide 7 by 7 to get 1.

$$1-\frac{9}{7}n$$