Solve for x 3 1/3-x=8/9

$3 \frac{1}{3} - x = \frac{8}{9}$

Simplify the left side.

Convert $3 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$3 + \frac{1}{3} - x = \frac{8}{9}$

Add $3$ and $\frac{1}{3}$ .

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

$3 \cdot \frac{3}{3} + \frac{1}{3} - x = \frac{8}{9}$

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

$\frac{3 \cdot 3}{3} + \frac{1}{3} - x = \frac{8}{9}$

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 1}{3} - x = \frac{8}{9}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} - x = \frac{8}{9}$

Add $9$ and $1$ .

$\frac{10}{3} - x = \frac{8}{9}$

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

Subtract $\frac{10}{3}$ from both sides of the equation.

$- x = \frac{8}{9} - \frac{10}{3}$

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

$- x = \frac{8}{9} - \frac{10}{3} \cdot \frac{3}{3}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$- x = \frac{8}{9} - \frac{10 \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$- x = \frac{8}{9} - \frac{10 \cdot 3}{9}$

Combine the numerators over the common denominator.

$- x = \frac{8 - 10 \cdot 3}{9}$

Simplify the numerator.

Multiply $- 10$ by $3$ .

$- x = \frac{8 - 30}{9}$

Subtract $30$ from $8$ .

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

Move the negative in front of the fraction.

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

Divide each term in $- x = - \frac{22}{9}$ by $- 1$ and simplify.

Divide each term in $- x = - \frac{22}{9}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \frac{22}{9}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \frac{22}{9}}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- \frac{22}{9}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{\frac{22}{9}}{1}$

Divide $\frac{22}{9}$ by $1$ .

$x = \frac{22}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{22}{9}$

Decimal Form:

$x = 2.\overline{4}$

Mixed Number Form:

$x = 2 \frac{4}{9}$

Solve for x 3 1/3-x=8/9

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