Solve for x 10/11-2/3=x/9

$\frac{10}{11} - \frac{2}{3} = \frac{x}{9}$

Step 1

Rewrite the equation as $\frac{x}{9} = \frac{10}{11} - \frac{2}{3}$ .

$\frac{x}{9} = \frac{10}{11} - \frac{2}{3}$

Step 2

Multiply both sides of the equation by $9$ .

$9 \frac{x}{9} = 9 (\frac{10}{11} - \frac{2}{3})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \frac{x}{9} = 9 (\frac{10}{11} - \frac{2}{3})$

Rewrite the expression.

$x = 9 (\frac{10}{11} - \frac{2}{3})$

Simplify the right side.

Simplify $9 (\frac{10}{11} - \frac{2}{3})$ .

To write $\frac{10}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 9 (\frac{10}{11} \cdot \frac{3}{3} - \frac{2}{3})$

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = 9 (\frac{10}{11} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{11}{11})$

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

Multiply $\frac{10}{11}$ by $\frac{3}{3}$ .

$x = 9 (\frac{10 \cdot 3}{11 \cdot 3} - \frac{2}{3} \cdot \frac{11}{11})$

Multiply $11$ by $3$ .

$x = 9 (\frac{10 \cdot 3}{33} - \frac{2}{3} \cdot \frac{11}{11})$

Multiply $\frac{2}{3}$ by $\frac{11}{11}$ .

$x = 9 (\frac{10 \cdot 3}{33} - \frac{2 \cdot 11}{3 \cdot 11})$

Multiply $3$ by $11$ .

$x = 9 (\frac{10 \cdot 3}{33} - \frac{2 \cdot 11}{33})$

Combine the numerators over the common denominator.

$x = 9 \frac{10 \cdot 3 - 2 \cdot 11}{33}$

Simplify the numerator.

Multiply $10$ by $3$ .

$x = 9 \frac{30 - 2 \cdot 11}{33}$

Multiply $- 2$ by $11$ .

$x = 9 \frac{30 - 22}{33}$

Subtract $22$ from $30$ .

$x = 9 (\frac{8}{33})$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x = 3 (3) \frac{8}{33}$

Factor $3$ out of $33$ .

$x = 3 \cdot 3 \frac{8}{3 \cdot 11}$

Cancel the common factor.

$x = 3 \cdot 3 \frac{8}{3 \cdot 11}$

Rewrite the expression.

$x = 3 (\frac{8}{11})$

Combine $3$ and $\frac{8}{11}$ .

$x = \frac{3 \cdot 8}{11}$

Multiply $3$ by $8$ .

$x = \frac{24}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{11}$

Decimal Form:

$x = 2.\overline{18}$

Mixed Number Form:

$x = 2 \frac{2}{11}$

Solve for x 10/11-2/3=x/9

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