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

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

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.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 Y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

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.

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