Solve y=a(1+x)

$$y = a ( 1 + x )$$

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 1+x.

$$y=a+ax$$

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

$$a+ax=y$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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

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 1+x.

$$y=a+ax$$

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

$$a+ax=y$$

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.

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