Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{7}$ and $n$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $- 3 \frac{3 n}{7}$ .

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Step 1.3.1

Combine $- 3$ and $\frac{3 n}{7}$ .

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

Step 1.3.2

Multiply $3$ by $- 3$ .

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

Step 1.4

Multiply $- 3 (- \frac{2}{7})$ .

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Step 1.4.1

Multiply $- 1$ by $- 3$ .

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

Step 1.4.2

Combine $3$ and $\frac{2}{7}$ .

$\frac{1}{7} + \frac{- 9 n}{7} + \frac{3 \cdot 2}{7}$

Step 1.4.3

Multiply $3$ by $2$ .

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

Step 1.5

Move the negative in front of the fraction.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $1$ and $6$ .

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

Step 2.3

Factor $- 1$ out of $- 9 n$ .

$\frac{- (9 n) + 7}{7}$

Step 2.4

Rewrite $7$ as $- 1 (- 7)$ .

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

Step 2.5

Factor $- 1$ out of $- (9 n) - 1 (- 7)$ .

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

Step 2.6

Simplify the expression.

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Step 2.6.1

Rewrite $- (9 n - 7)$ as $- 1 (9 n - 7)$ .

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

Step 2.6.2

Move the negative in front of the fraction.

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