Solve for x 9/11-1/3=x/9

$\frac{9}{11} - \frac{1}{3} = \frac{x}{9}$

Rewrite the equation as $\frac{x}{9} = \frac{9}{11} - \frac{1}{3}$ .

$\frac{x}{9} = \frac{9}{11} - \frac{1}{3}$

Multiply both sides of the equation by $9$ .

$9 \cdot \frac{x}{9} = 9 \cdot (\frac{9}{11} - \frac{1}{3})$

Simplify both sides of the equation.

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Cancel the common factor of $9$ .

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Cancel the common factor.

$9 \cdot \frac{x}{9} = 9 \cdot (\frac{9}{11} - \frac{1}{3})$

Rewrite the expression.

$x = 9 \cdot (\frac{9}{11} - \frac{1}{3})$

Simplify $9 \cdot (\frac{9}{11} - \frac{1}{3})$ .

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To write $\frac{9}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 9 \cdot (\frac{9}{11} \cdot \frac{3}{3} - \frac{1}{3})$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = 9 \cdot (\frac{9}{11} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{11}{11})$

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{9}{11}$ and $\frac{3}{3}$ .

$x = 9 \cdot (\frac{9 \cdot 3}{11 \cdot 3} - \frac{1}{3} \cdot \frac{11}{11})$

Multiply $11$ by $3$ .

$x = 9 \cdot (\frac{9 \cdot 3}{33} - \frac{1}{3} \cdot \frac{11}{11})$

Multiply $\frac{1}{3}$ and $\frac{11}{11}$ .

$x = 9 \cdot (\frac{9 \cdot 3}{33} - \frac{11}{3 \cdot 11})$

Multiply $3$ by $11$ .

$x = 9 \cdot (\frac{9 \cdot 3}{33} - \frac{11}{33})$

Combine the numerators over the common denominator.

$x = 9 \cdot \frac{9 \cdot 3 - 11}{33}$

Simplify the numerator.

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Multiply $9$ by $3$ .

$x = 9 \cdot \frac{27 - 11}{33}$

Subtract $11$ from $27$ .

$x = 9 \cdot \frac{16}{33}$

Cancel the common factor of $3$ .

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Factor $3$ out of $9$ .

$x = 3 (3) \cdot \frac{16}{33}$

Factor $3$ out of $33$ .

$x = 3 \cdot 3 \cdot \frac{16}{3 \cdot 11}$

Cancel the common factor.

$x = 3 \cdot 3 \cdot \frac{16}{3 \cdot 11}$

Rewrite the expression.

$x = 3 \cdot \frac{16}{11}$

Combine $3$ and $\frac{16}{11}$ .

$x = \frac{3 \cdot 16}{11}$

Multiply $3$ by $16$ .

$x = \frac{48}{11}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{48}{11}$

Decimal Form:

$x = 4.\overline{36}$

Mixed Number Form:

$x = 4 \frac{4}{11}$

Solve for x 9/11-1/3=x/9

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