Solve for x 2/3x-3/5+x=1/15-1/3x

$\frac{2}{3} x - \frac{3}{5} + x = \frac{1}{15} - \frac{1}{3} x$

Simplify $\frac{2}{3} x - \frac{3}{5} + x$ .

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} - \frac{3}{5} + x = \frac{1}{15} - \frac{1}{3} x$

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

$\frac{2 x}{3} + x \cdot \frac{3}{3} - \frac{3}{5} = \frac{1}{15} - \frac{1}{3} x$

Combine $x$ and $\frac{3}{3}$ .

$\frac{2 x}{3} + \frac{x \cdot 3}{3} - \frac{3}{5} = \frac{1}{15} - \frac{1}{3} x$

Combine the numerators over the common denominator.

$\frac{2 x + x \cdot 3}{3} - \frac{3}{5} = \frac{1}{15} - \frac{1}{3} x$

Add $2 x$ and $x \cdot 3$ .

Reorder $x$ and $3$ .

$\frac{2 x + 3 \cdot x}{3} - \frac{3}{5} = \frac{1}{15} - \frac{1}{3} x$

Add $2 x$ and $3 \cdot x$ .

$\frac{5 x}{3} - \frac{3}{5} = \frac{1}{15} - \frac{1}{3} x$

Combine $x$ and $\frac{1}{3}$ .

$\frac{5 x}{3} - \frac{3}{5} = \frac{1}{15} - \frac{x}{3}$

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

Add $\frac{x}{3}$ to both sides of the equation.

$\frac{5 x}{3} - \frac{3}{5} + \frac{x}{3} = \frac{1}{15}$

Combine the numerators over the common denominator.

$\frac{5 x + x}{3} + \frac{- 3}{5} = \frac{1}{15}$

Add $5 x$ and $x$ .

$\frac{6 x}{3} + \frac{- 3}{5} = \frac{1}{15}$

Simplify each term.

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x$ .

$\frac{3 (2 x)}{3} + \frac{- 3}{5} = \frac{1}{15}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 x)}{3 (1)} + \frac{- 3}{5} = \frac{1}{15}$

Cancel the common factor.

$\frac{3 (2 x)}{3 \cdot 1} + \frac{- 3}{5} = \frac{1}{15}$

Rewrite the expression.

$\frac{2 x}{1} + \frac{- 3}{5} = \frac{1}{15}$

Divide $2 x$ by $1$ .

$2 x + \frac{- 3}{5} = \frac{1}{15}$

Move the negative in front of the fraction.

$2 x - \frac{3}{5} = \frac{1}{15}$

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

Add $\frac{3}{5}$ to both sides of the equation.

$2 x = \frac{1}{15} + \frac{3}{5}$

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

$2 x = \frac{1}{15} + \frac{3}{5} \cdot \frac{3}{3}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

$2 x = \frac{1}{15} + \frac{3 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$2 x = \frac{1}{15} + \frac{3 \cdot 3}{15}$

Combine the numerators over the common denominator.

$2 x = \frac{1 + 3 \cdot 3}{15}$

Simplify the numerator.

Multiply $3$ by $3$ .

$2 x = \frac{1 + 9}{15}$

Add $1$ and $9$ .

$2 x = \frac{10}{15}$

Cancel the common factor of $10$ and $15$ .

Factor $5$ out of $10$ .

$2 x = \frac{5 (2)}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$

Solve for x 2/3x-3/5+x=1/15-1/3x

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