Solve 3/4z-1/4z+1=2/4z+1

$$\frac { 3 } { 4 } z - \frac { 1 } { 4 } z + 1 = \frac { 2 } { 4 } z + 1$$

Solve for z (complex solution)

$$z\in \mathrm{C}$$

Solution Steps

Combine \frac{3}{4}z and -\frac{1}{4}z to get \frac{1}{2}z.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{2}z from both sides.

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

Combine \frac{1}{2}z and -\frac{1}{2}z to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any z.

$$z\in \mathrm{C}$$

Solve for z

$$z\in \mathrm{R}$$

Solution Steps

Combine \frac{3}{4}z and -\frac{1}{4}z to get \frac{1}{2}z.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{2}z from both sides.

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

Combine \frac{1}{2}z and -\frac{1}{2}z to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any z.

$$z\in \mathrm{R}$$