Solve w=x-y+z/8

$$w = \frac { x - y + z } { 8 }$$

Solve for x

$$x=y-z+8w$$

Steps for Solving Linear Equation

Divide each term of x-y+z by 8 to get \frac{1}{8}x-\frac{1}{8}y+\frac{1}{8}z.

$$w=\frac{1}{8}x-\frac{1}{8}y+\frac{1}{8}z$$

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

$$\frac{1}{8}x-\frac{1}{8}y+\frac{1}{8}z=w$$

Add \frac{1}{8}y to both sides.

$$\frac{1}{8}x+\frac{1}{8}z=w+\frac{1}{8}y$$

Subtract \frac{1}{8}z from both sides.

$$\frac{1}{8}x=w+\frac{1}{8}y-\frac{1}{8}z$$

The equation is in standard form.

$$\frac{1}{8}x=\frac{y}{8}-\frac{z}{8}+w$$

Multiply both sides by 8.

$$\frac{\frac{1}{8}x}{\frac{1}{8}}=\frac{\frac{y}{8}-\frac{z}{8}+w}{\frac{1}{8}}$$

Dividing by \frac{1}{8} undoes the multiplication by \frac{1}{8}.

$$x=\frac{\frac{y}{8}-\frac{z}{8}+w}{\frac{1}{8}}$$

Divide w+\frac{y}{8}-\frac{z}{8} by \frac{1}{8} by multiplying w+\frac{y}{8}-\frac{z}{8} by the reciprocal of \frac{1}{8}.

$$x=y-z+8w$$

Solve for w

$$w=\frac{x-y+z}{8}$$

Solution Steps

Divide each term of x-y+z by 8 to get \frac{1}{8}x-\frac{1}{8}y+\frac{1}{8}z.

$$w=\frac{1}{8}x-\frac{1}{8}y+\frac{1}{8}z$$