Solve y=a(1-2x)

$$y = a ( 1 - 2 x )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{1-2x}\text{, }&x\neq \frac{1}{2}\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-2x.

$$y=a-2ax$$

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

$$a-2ax=y$$

Combine all terms containing a.

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

Divide both sides by 1-2x.

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

Dividing by 1-2x undoes the multiplication by 1-2x.

$$a=\frac{y}{1-2x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y}{2a}+\frac{1}{2}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-2x.

$$y=a-2ax$$

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

$$a-2ax=y$$

Subtract a from both sides.

$$-2ax=y-a$$

The equation is in standard form.

$$\left(-2a\right)x=y-a$$

Divide both sides by -2a.

$$\frac{\left(-2a\right)x}{-2a}=\frac{y-a}{-2a}$$

Dividing by -2a undoes the multiplication by -2a.

$$x=\frac{y-a}{-2a}$$

Divide y-a by -2a.

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

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{1-2x}\text{, }&x\neq \frac{1}{2}\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-2x.

$$y=a-2ax$$

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

$$a-2ax=y$$

Combine all terms containing a.

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

Divide both sides by 1-2x.

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

Dividing by 1-2x undoes the multiplication by 1-2x.

$$a=\frac{y}{1-2x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y}{2a}+\frac{1}{2}\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-2x.

$$y=a-2ax$$

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

$$a-2ax=y$$

Subtract a from both sides.

$$-2ax=y-a$$

The equation is in standard form.

$$\left(-2a\right)x=y-a$$

Divide both sides by -2a.

$$\frac{\left(-2a\right)x}{-2a}=\frac{y-a}{-2a}$$

Dividing by -2a undoes the multiplication by -2a.

$$x=\frac{y-a}{-2a}$$

Divide y-a by -2a.

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