Solve r=alpha(1-x)

$$r = \alpha ( 1 - x )$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply \alpha by 1-x.

$$r=\alpha -\alpha x$$

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

$$\alpha -\alpha x=r$$

Subtract \alpha from both sides.

$$-\alpha x=r-\alpha$$

The equation is in standard form.

$$\left(-\alpha \right)x=r-\alpha$$

Divide both sides by -\alpha .

$$\frac{\left(-\alpha \right)x}{-\alpha }=\frac{r-\alpha }{-\alpha }$$

Dividing by -\alpha undoes the multiplication by -\alpha .

$$x=\frac{r-\alpha }{-\alpha }$$

Divide r-\alpha by -\alpha .

$$x=-\frac{r}{\alpha }+1$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \alpha by 1-x.

$$r=\alpha -\alpha x$$

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

$$\alpha -\alpha x=r$$

Subtract \alpha from both sides.

$$-\alpha x=r-\alpha$$

The equation is in standard form.

$$\left(-\alpha \right)x=r-\alpha$$

Divide both sides by -\alpha .

$$\frac{\left(-\alpha \right)x}{-\alpha }=\frac{r-\alpha }{-\alpha }$$

Dividing by -\alpha undoes the multiplication by -\alpha .

$$x=\frac{r-\alpha }{-\alpha }$$

Divide r-\alpha by -\alpha .

$$x=-\frac{r}{\alpha }+1$$

Solve for r

$$r=\alpha \left(1-x\right)$$

Solution Steps

Use the distributive property to multiply \alpha by 1-x.

$$r=\alpha -\alpha x$$