Solve 3x+y+1+180-(3x+y+1)=180

$$3x+y+1+180-(3x+y+1)=180$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Add 1 and 180 to get 181.

$$3x+y+181-\left(3x+y+1\right)=180$$

To find the opposite of 3x+y+1, find the opposite of each term.

$$3x+y+181-3x-y-1=180$$

Combine 3x and -3x to get 0.

$$y+181-y-1=180$$

Combine y and -y to get 0.

$$181-1=180$$

Subtract 1 from 181 to get 180.

$$180=180$$

Compare 180 and 180.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

Add 1 and 180 to get 181.

$$3x+y+181-\left(3x+y+1\right)=180$$

To find the opposite of 3x+y+1, find the opposite of each term.

$$3x+y+181-3x-y-1=180$$

Combine 3x and -3x to get 0.

$$y+181-y-1=180$$

Combine y and -y to get 0.

$$181-1=180$$

Subtract 1 from 181 to get 180.

$$180=180$$

Compare 180 and 180.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Add 1 and 180 to get 181.

$$3x+y+181-\left(3x+y+1\right)=180$$

To find the opposite of 3x+y+1, find the opposite of each term.

$$3x+y+181-3x-y-1=180$$

Combine 3x and -3x to get 0.

$$y+181-y-1=180$$

Combine y and -y to get 0.

$$181-1=180$$

Subtract 1 from 181 to get 180.

$$180=180$$

Compare 180 and 180.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

Add 1 and 180 to get 181.

$$3x+y+181-\left(3x+y+1\right)=180$$

To find the opposite of 3x+y+1, find the opposite of each term.

$$3x+y+181-3x-y-1=180$$

Combine 3x and -3x to get 0.

$$y+181-y-1=180$$

Combine y and -y to get 0.

$$181-1=180$$

Subtract 1 from 181 to get 180.

$$180=180$$

Compare 180 and 180.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$