Solve for n 5/6=(7n+9)/9

$\frac{5}{6} = \frac{7 n + 9}{9}$

Rewrite the equation as $\frac{7 n + 9}{9} = \frac{5}{6}$ .

$\frac{7 n + 9}{9} = \frac{5}{6}$

Multiply both sides of the equation by $9$ .

$7 n + 9 = \frac{5}{6} \cdot (9)$

Remove parentheses.

$7 n + 9 = \frac{5}{6} \cdot (9)$

Simplify $\frac{5}{6} \cdot (9)$ .

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Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$7 n + 9 = \frac{5}{3 (2)} \cdot 9$

Factor $3$ out of $9$ .

$7 n + 9 = \frac{5}{3 \cdot 2} \cdot (3 \cdot 3)$

Cancel the common factor.

$7 n + 9 = \frac{5}{3 \cdot 2} \cdot (3 \cdot 3)$

Rewrite the expression.

$7 n + 9 = \frac{5}{2} \cdot 3$

Combine $\frac{5}{2}$ and $3$ .

$7 n + 9 = \frac{5 \cdot 3}{2}$

Multiply $5$ by $3$ .

$7 n + 9 = \frac{15}{2}$

Move all terms not containing $n$ to the right side of the equation.

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Subtract $9$ from both sides of the equation.

$7 n = \frac{15}{2} - 9$

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 n = \frac{15}{2} - 9 \cdot \frac{2}{2}$

Combine $- 9$ and $\frac{2}{2}$ .

$7 n = \frac{15}{2} + \frac{- 9 \cdot 2}{2}$

Combine the numerators over the common denominator.

$7 n = \frac{15 - 9 \cdot 2}{2}$

Simplify the numerator.

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Multiply $- 9$ by $2$ .

$7 n = \frac{15 - 18}{2}$

Subtract $18$ from $15$ .

$7 n = \frac{- 3}{2}$

Move the negative in front of the fraction.

$7 n = - \frac{3}{2}$

Divide each term by $7$ and simplify.

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Divide each term in $7 n = - \frac{3}{2}$ by $7$ .

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

Cancel the common factor of $7$ .

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Cancel the common factor.

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

Divide $n$ by $1$ .

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

Multiply $- \frac{3}{2} \cdot \frac{1}{7}$ .

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Multiply $\frac{1}{7}$ and $\frac{3}{2}$ .

$n = - \frac{3}{7 \cdot 2}$

Multiply $7$ by $2$ .

$n = - \frac{3}{14}$

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{3}{14}$

Decimal Form:

$n = - 0.2\overline{142857}$

Solve for n 5/6=(7n+9)/9

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