Solve for x 5/9-x/3=4/9

$\frac{5}{9} - \frac{x}{3} = \frac{4}{9}$

Step 1

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

Subtract $\frac{5}{9}$ from both sides of the equation.

$- \frac{x}{3} = \frac{4}{9} - \frac{5}{9}$

Combine the numerators over the common denominator.

$- \frac{x}{3} = \frac{4 - 5}{9}$

Subtract $5$ from $4$ .

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

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- 3$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{9}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$

Solve for x 5/9-x/3=4/9

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