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.

$\frac{3}{2} \cdot \frac{2 y}{3} + \frac{3}{2} \cdot \frac{2 z}{3} = \frac{3}{2} X$

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.

$z = \frac{3 X}{2} - y$