Solve for Z x=2/3(Y-Z)

$x = \frac{2}{3} (Y - Z)$

Rewrite the equation as $\frac{2}{3} \cdot (Y - Z) = x$ .

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

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (Y - Z))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} Y + \frac{2}{3} (- Z)) = \frac{3}{2} x$

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

$\frac{3}{2} (\frac{2 Y}{3} + \frac{2}{3} (- Z)) = \frac{3}{2} x$

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

$\frac{3}{2} (\frac{2 Y}{3} - \frac{2 Z}{3}) = \frac{3}{2} x$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 Y}{3} + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 Y}{3} + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Rewrite the expression.

$\frac{1}{2} (2 Y) + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Cancel the common factor of $2$ .

Factor $2$ out of $2 Y$ .

$\frac{1}{2} (2 (Y)) + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Cancel the common factor.

$\frac{1}{2} (2 Y) + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Rewrite the expression.

$Y + \frac{3}{2} (- \frac{2 Z}{3}) = \frac{3}{2} x$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2 Z}{3}$ into the numerator.

$Y + \frac{3}{2} \cdot \frac{- 2 Z}{3} = \frac{3}{2} x$

Cancel the common factor.

$Y + \frac{3}{2} \cdot \frac{- 2 Z}{3} = \frac{3}{2} x$

Rewrite the expression.

$Y + \frac{1}{2} (- 2 Z) = \frac{3}{2} x$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 Z$ .

$Y + \frac{1}{2} (2 (- Z)) = \frac{3}{2} x$

Cancel the common factor.

$Y + \frac{1}{2} (2 (- Z)) = \frac{3}{2} x$

Rewrite the expression.

$Y - Z = \frac{3}{2} x$

Simplify the right side.

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

$Y - Z = \frac{3 x}{2}$

Subtract $Y$ from both sides of the equation.

$- Z = \frac{3 x}{2} - Y$

Divide each term in $- Z = \frac{3 x}{2} - Y$ by $- 1$ and simplify.

Divide each term in $- Z = \frac{3 x}{2} - Y$ by $- 1$ .

$\frac{- Z}{- 1} = \frac{\frac{3 x}{2}}{- 1} + \frac{- Y}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{Z}{1} = \frac{\frac{3 x}{2}}{- 1} + \frac{- Y}{- 1}$

Divide $Z$ by $1$ .

$Z = \frac{\frac{3 x}{2}}{- 1} + \frac{- Y}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{3 x}{2}}{- 1}$ .

$Z = - 1 \cdot \frac{3 x}{2} + \frac{- Y}{- 1}$

Rewrite $- 1 \cdot \frac{3 x}{2}$ as $- \frac{3 x}{2}$ .

$Z = - \frac{3 x}{2} + \frac{- Y}{- 1}$

Dividing two negative values results in a positive value.

$Z = - \frac{3 x}{2} + \frac{Y}{1}$

Divide $Y$ by $1$ .

$Z = - \frac{3 x}{2} + Y$

Solve for Z x=2/3(Y-Z)

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