Solve X=2/9(Y-Z)

$$X = \frac { 2 } { 9 } ( Y - Z )$$

Solve for Y

$$Y=\frac{9X}{2}+Z$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{9} by Y-Z.

$$X=\frac{2}{9}Y-\frac{2}{9}Z$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2}{9}Y-\frac{2}{9}Z=X$$

Add \frac{2}{9}Z to both sides.

$$\frac{2}{9}Y=X+\frac{2}{9}Z$$

The equation is in standard form.

$$\frac{2}{9}Y=\frac{2Z}{9}+X$$

Divide both sides of the equation by \frac{2}{9}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{9}Y}{\frac{2}{9}}=\frac{\frac{2Z}{9}+X}{\frac{2}{9}}$$

Dividing by \frac{2}{9} undoes the multiplication by \frac{2}{9}.

$$Y=\frac{\frac{2Z}{9}+X}{\frac{2}{9}}$$

Divide X+\frac{2Z}{9} by \frac{2}{9} by multiplying X+\frac{2Z}{9} by the reciprocal of \frac{2}{9}.

$$Y=\frac{9X}{2}+Z$$

Solve for X

$$X=\frac{2\left(Y-Z\right)}{9}$$

Solution Steps

Use the distributive property to multiply \frac{2}{9} by Y-Z.

$$X=\frac{2}{9}Y-\frac{2}{9}Z$$