Solve 1/4x-2=1/4+z

$$\frac{ 1 }{ 4 } x-2= \frac{ 1 }{ 4 } +z$$

Solve for x

$$x=4z+9$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$\frac{1}{4}x=\frac{1}{4}+z+2$$

Add \frac{1}{4} and 2 to get \frac{9}{4}.

$$\frac{1}{4}x=\frac{9}{4}+z$$

The equation is in standard form.

$$\frac{1}{4}x=z+\frac{9}{4}$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{z+\frac{9}{4}}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$x=\frac{z+\frac{9}{4}}{\frac{1}{4}}$$

Divide \frac{9}{4}+z by \frac{1}{4} by multiplying \frac{9}{4}+z by the reciprocal of \frac{1}{4}.

$$x=4z+9$$

Solve for z

$$z=\frac{x-9}{4}$$

Solution Steps

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

$$\frac{1}{4}+z=\frac{1}{4}x-2$$

Subtract \frac{1}{4} from both sides.

$$z=\frac{1}{4}x-2-\frac{1}{4}$$

Subtract \frac{1}{4} from -2 to get -\frac{9}{4}.

$$z=\frac{1}{4}x-\frac{9}{4}$$