Solve varepsilon-k_{z}=k_{q}+xvarepsilon

$$\varepsilon - k _ { z } = k _ { q } + x \varepsilon$$

Solve for k_q

$$k_{q}=-x\epsilon +\epsilon -k_{z}$$

Solution Steps

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

$$k_{q}+x\epsilon =\epsilon -k_{z}$$

Subtract x\epsilon from both sides.

$$k_{q}=\epsilon -k_{z}-x\epsilon$$

Solve for k_z

$$k_{z}=-x\epsilon +\epsilon -k_{q}$$

Steps for Solving Linear Equation

Subtract \epsilon from both sides.

$$-k_{z}=k_{q}+x\epsilon -\epsilon$$

The equation is in standard form.

$$-k_{z}=x\epsilon +k_{q}-\epsilon$$

Divide both sides by -1.

$$\frac{-k_{z}}{-1}=\frac{x\epsilon +k_{q}-\epsilon }{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k_{z}=\frac{x\epsilon +k_{q}-\epsilon }{-1}$$

Divide -\epsilon +k_{q}+x\epsilon by -1.

$$k_{z}=-x\epsilon +\epsilon -k_{q}$$