Solve for z x=2/9(y-z)

$x = \frac{2}{9} (y - z)$

Step 1

Rewrite the equation as $\frac{2}{9} \cdot (y - z) = x$ .

$\frac{2}{9} \cdot (y - z) = x$

Step 2

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} (\frac{2}{9} \cdot (y - z)) = \frac{9}{2} x$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{9}{2} (\frac{2}{9} \cdot (y - z))$ .

Apply the distributive property.

$\frac{9}{2} (\frac{2}{9} y + \frac{2}{9} (- z)) = \frac{9}{2} x$

Combine $\frac{2}{9}$ and $y$ .

$\frac{9}{2} (\frac{2 y}{9} + \frac{2}{9} (- z)) = \frac{9}{2} x$

Combine $\frac{2}{9}$ and $z$ .

$\frac{9}{2} (\frac{2 y}{9} - \frac{2 z}{9}) = \frac{9}{2} x$

Apply the distributive property.

$\frac{9}{2} \cdot \frac{2 y}{9} + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 y}{9} + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Rewrite the expression.

$\frac{1}{2} (2 y) + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Cancel the common factor.

$\frac{1}{2} (2 y) + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Rewrite the expression.

$y + \frac{9}{2} (- \frac{2 z}{9}) = \frac{9}{2} x$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{2 z}{9}$ into the numerator.

$y + \frac{9}{2} \cdot \frac{- 2 z}{9} = \frac{9}{2} x$

Cancel the common factor.

$y + \frac{9}{2} \cdot \frac{- 2 z}{9} = \frac{9}{2} x$

Rewrite the expression.

$y + \frac{1}{2} (- 2 z) = \frac{9}{2} x$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 z$ .

$y + \frac{1}{2} (2 (- z)) = \frac{9}{2} x$

Cancel the common factor.

$y + \frac{1}{2} (2 (- z)) = \frac{9}{2} x$

Rewrite the expression.

$y - z = \frac{9}{2} x$

Simplify the right side.

Combine $\frac{9}{2}$ and $x$ .

$y - z = \frac{9 x}{2}$

Step 4

Subtract $y$ from both sides of the equation.

$- z = \frac{9 x}{2} - y$

Step 5

Divide each term in $- z = \frac{9 x}{2} - y$ by $- 1$ and simplify.

Divide each term in $- z = \frac{9 x}{2} - y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{\frac{9 x}{2}}{- 1} + \frac{- y}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{\frac{9 x}{2}}{- 1} + \frac{- y}{- 1}$

Divide $z$ by $1$ .

$z = \frac{\frac{9 x}{2}}{- 1} + \frac{- y}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{9 x}{2}}{- 1}$ .

$z = - 1 \cdot \frac{9 x}{2} + \frac{- y}{- 1}$

Rewrite $- 1 \cdot \frac{9 x}{2}$ as $- \frac{9 x}{2}$ .

$z = - \frac{9 x}{2} + \frac{- y}{- 1}$

Dividing two negative values results in a positive value.

$z = - \frac{9 x}{2} + \frac{y}{1}$

Divide $y$ by $1$ .

$z = - \frac{9 x}{2} + y$

Solve for z x=2/9(y-z)

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