Solve y=a(x+1

$$y = a ( x + 1$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$y=ax+a$$

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

$$ax+a=y$$

Combine all terms containing a.

$$\left(x+1\right)a=y$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{y}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$a=\frac{y}{x+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y}{a}-1\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$y=ax+a$$

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

$$ax+a=y$$

Subtract a from both sides.

$$ax=y-a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{y-a}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{y-a}{a}$$

Divide y-a by a.

$$x=\frac{y}{a}-1$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$y=ax+a$$

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

$$ax+a=y$$

Combine all terms containing a.

$$\left(x+1\right)a=y$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{y}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$a=\frac{y}{x+1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y}{a}-1\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$y=ax+a$$

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

$$ax+a=y$$

Subtract a from both sides.

$$ax=y-a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{y-a}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{y-a}{a}$$

Divide y-a by a.

$$x=\frac{y}{a}-1$$