Solve y=(1+2m)x+2

$$y = ( 1 + 2 m ) x + 2$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{x-y+2}{2x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2m by x.

$$y=x+2mx+2$$

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

$$x+2mx+2=y$$

Subtract x from both sides.

$$2mx+2=y-x$$

Subtract 2 from both sides.

$$2mx=y-x-2$$

The equation is in standard form.

$$2xm=-x+y-2$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{-x+y-2}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{-x+y-2}{2x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2-y}{2m+1}\text{, }&m\neq -\frac{1}{2}\\x\in \mathrm{C}\text{, }&y=2\text{ and }m=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2m by x.

$$y=x+2mx+2$$

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

$$x+2mx+2=y$$

Subtract 2 from both sides.

$$x+2mx=y-2$$

Combine all terms containing x.

$$\left(1+2m\right)x=y-2$$

The equation is in standard form.

$$\left(2m+1\right)x=y-2$$

Divide both sides by 1+2m.

$$\frac{\left(2m+1\right)x}{2m+1}=\frac{y-2}{2m+1}$$

Dividing by 1+2m undoes the multiplication by 1+2m.

$$x=\frac{y-2}{2m+1}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{x-y+2}{2x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2m by x.

$$y=x+2mx+2$$

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

$$x+2mx+2=y$$

Subtract x from both sides.

$$2mx+2=y-x$$

Subtract 2 from both sides.

$$2mx=y-x-2$$

The equation is in standard form.

$$2xm=-x+y-2$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{-x+y-2}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{-x+y-2}{2x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2-y}{2m+1}\text{, }&m\neq -\frac{1}{2}\\x\in \mathrm{R}\text{, }&y=2\text{ and }m=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2m by x.

$$y=x+2mx+2$$

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

$$x+2mx+2=y$$

Subtract 2 from both sides.

$$x+2mx=y-2$$

Combine all terms containing x.

$$\left(1+2m\right)x=y-2$$

The equation is in standard form.

$$\left(2m+1\right)x=y-2$$

Divide both sides by 1+2m.

$$\frac{\left(2m+1\right)x}{2m+1}=\frac{y-2}{2m+1}$$

Dividing by 1+2m undoes the multiplication by 1+2m.

$$x=\frac{y-2}{2m+1}$$