Solve for x x/5+2/3=x/9

$\frac{x}{5} + \frac{2}{3} = \frac{x}{9}$

Multiply both sides by $9$ .

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

Simplify.

Simplify the left side.

Simplify $(\frac{x}{5} + \frac{2}{3}) \cdot 9$ .

Simplify terms.

Apply the distributive property.

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

Combine $\frac{x}{5}$ and $9$ .

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

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $3$ .

$\frac{x \cdot 9}{5} + 6 = \frac{x}{9} \cdot 9$

Move $9$ to the left of $x$ .

$\frac{9 x}{5} + 6 = \frac{x}{9} \cdot 9$

Simplify the right side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{5} + 6 = \frac{x}{9} \cdot 9$

Rewrite the expression.

$\frac{9 x}{5} + 6 = x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\frac{9 x}{5} + 6 - x = 0$

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

$\frac{9 x}{5} - x \cdot \frac{5}{5} + 6 = 0$

Combine $- x$ and $\frac{5}{5}$ .

$\frac{9 x}{5} + \frac{- x \cdot 5}{5} + 6 = 0$

Combine the numerators over the common denominator.

$\frac{9 x - x \cdot 5}{5} + 6 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $9 x - x \cdot 5$ .

Factor $x$ out of $9 x$ .

$\frac{x \cdot 9 - x \cdot 5}{5} + 6 = 0$

Factor $x$ out of $- x \cdot 5$ .

$\frac{x \cdot 9 + x (- 1 \cdot 5)}{5} + 6 = 0$

Factor $x$ out of $x \cdot 9 + x (- 1 \cdot 5)$ .

$\frac{x (9 - 1 \cdot 5)}{5} + 6 = 0$

Multiply $- 1$ by $5$ .

$\frac{x (9 - 5)}{5} + 6 = 0$

Subtract $5$ from $9$ .

$\frac{x \cdot 4}{5} + 6 = 0$

Move $4$ to the left of $x$ .

$\frac{4 x}{5} + 6 = 0$

Subtract $6$ from both sides of the equation.

$\frac{4 x}{5} = - 6$

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot - 6$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{4} \cdot \frac{4 x}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} \cdot - 6$

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot - 6$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{5}{4} \cdot - 6$

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{5}{4} \cdot - 6$

Rewrite the expression.

$x = \frac{5}{4} \cdot - 6$

Simplify the right side.

Simplify $\frac{5}{4} \cdot - 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{5}{2 (2)} \cdot - 6$

Factor $2$ out of $- 6$ .

$x = \frac{5}{2 \cdot 2} \cdot (2 \cdot - 3)$

Cancel the common factor.

$x = \frac{5}{2 \cdot 2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$x = \frac{5}{2} \cdot - 3$

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

$x = \frac{5 \cdot - 3}{2}$

Simplify the expression.

Multiply $5$ by $- 3$ .

$x = \frac{- 15}{2}$

Move the negative in front of the fraction.

$x = - \frac{15}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{2}$

Decimal Form:

$x = - 7.5$

Mixed Number Form:

$x = - 7 \frac{1}{2}$

Solve for x x/5+2/3=x/9

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