Solve for x 5/7-1/3=x/9

$\frac{5}{7} - \frac{1}{3} = \frac{x}{9}$

Step 1

Rewrite the equation as $\frac{x}{9} = \frac{5}{7} - \frac{1}{3}$ .

$\frac{x}{9} = \frac{5}{7} - \frac{1}{3}$

Step 2

Multiply both sides of the equation by $9$ .

$9 \frac{x}{9} = 9 (\frac{5}{7} - \frac{1}{3})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \frac{x}{9} = 9 (\frac{5}{7} - \frac{1}{3})$

Rewrite the expression.

$x = 9 (\frac{5}{7} - \frac{1}{3})$

Simplify the right side.

Simplify $9 (\frac{5}{7} - \frac{1}{3})$ .

To write $\frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 9 (\frac{5}{7} \cdot \frac{3}{3} - \frac{1}{3})$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = 9 (\frac{5}{7} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{7}{7})$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{7}$ by $\frac{3}{3}$ .

$x = 9 (\frac{5 \cdot 3}{7 \cdot 3} - \frac{1}{3} \cdot \frac{7}{7})$

Multiply $7$ by $3$ .

$x = 9 (\frac{5 \cdot 3}{21} - \frac{1}{3} \cdot \frac{7}{7})$

Multiply $\frac{1}{3}$ by $\frac{7}{7}$ .

$x = 9 (\frac{5 \cdot 3}{21} - \frac{7}{3 \cdot 7})$

Multiply $3$ by $7$ .

$x = 9 (\frac{5 \cdot 3}{21} - \frac{7}{21})$

Combine the numerators over the common denominator.

$x = 9 \frac{5 \cdot 3 - 7}{21}$

Simplify the numerator.

Multiply $5$ by $3$ .

$x = 9 \frac{15 - 7}{21}$

Subtract $7$ from $15$ .

$x = 9 (\frac{8}{21})$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x = 3 (3) \frac{8}{21}$

Factor $3$ out of $21$ .

$x = 3 \cdot 3 \frac{8}{3 \cdot 7}$

Cancel the common factor.

$x = 3 \cdot 3 \frac{8}{3 \cdot 7}$

Rewrite the expression.

$x = 3 (\frac{8}{7})$

Combine $3$ and $\frac{8}{7}$ .

$x = \frac{3 \cdot 8}{7}$

Multiply $3$ by $8$ .

$x = \frac{24}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{7}$

Decimal Form:

$x = 3.\overline{428571}$

Mixed Number Form:

$x = 3 \frac{3}{7}$

Solve for x 5/7-1/3=x/9

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