Solve X=7/8(Y+Z)

$$X = \frac { 7 } { 8 } ( Y + Z )$$

Solve for Y

$$Y=\frac{8X}{7}-Z$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{8} by Y+Z.

$$X=\frac{7}{8}Y+\frac{7}{8}Z$$

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

$$\frac{7}{8}Y+\frac{7}{8}Z=X$$

Subtract \frac{7}{8}Z from both sides.

$$\frac{7}{8}Y=X-\frac{7}{8}Z$$

The equation is in standard form.

$$\frac{7}{8}Y=-\frac{7Z}{8}+X$$

Divide both sides of the equation by \frac{7}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{7}{8}Y}{\frac{7}{8}}=\frac{-\frac{7Z}{8}+X}{\frac{7}{8}}$$

Dividing by \frac{7}{8} undoes the multiplication by \frac{7}{8}.

$$Y=\frac{-\frac{7Z}{8}+X}{\frac{7}{8}}$$

Divide X-\frac{7Z}{8} by \frac{7}{8} by multiplying X-\frac{7Z}{8} by the reciprocal of \frac{7}{8}.

$$Y=\frac{8X}{7}-Z$$

Solve for X

$$X=\frac{7\left(Y+Z\right)}{8}$$

Solution Steps

Use the distributive property to multiply \frac{7}{8} by Y+Z.

$$X=\frac{7}{8}Y+\frac{7}{8}Z$$