Solve for n 7/9=2n+1/9

$\frac{7}{9} = 2 n + \frac{1}{9}$

Step 1

Rewrite the equation as $2 n + \frac{1}{9} = \frac{7}{9}$ .

$2 n + \frac{1}{9} = \frac{7}{9}$

Step 2

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

Subtract $\frac{1}{9}$ from both sides of the equation.

$2 n = \frac{7}{9} - \frac{1}{9}$

Combine the numerators over the common denominator.

$2 n = \frac{7 - 1}{9}$

Subtract $1$ from $7$ .

$2 n = \frac{6}{9}$

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$2 n = \frac{3 (2)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Divide each term in $2 n = \frac{2}{3}$ by $2$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$n = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{3}$

Decimal Form:

$n = 0.\overline{3}$

Solve for n 7/9=2n+1/9

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