Solve 3x-x/a=c

$$3 x - \frac { x } { a } = c$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{x}{c-3x}\text{, }&x\neq 0\text{ and }x\neq \frac{c}{3}\\a\neq 0\text{, }&x=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$3xa-x=ca$$

Subtract ca from both sides.

$$3xa-x-ca=0$$

Add x to both sides. Anything plus zero gives itself.

$$3xa-ca=x$$

Combine all terms containing a.

$$\left(3x-c\right)a=x$$

Divide both sides by 3x-c.

$$\frac{\left(3x-c\right)a}{3x-c}=\frac{x}{3x-c}$$

Dividing by 3x-c undoes the multiplication by 3x-c.

$$a=\frac{x}{3x-c}$$

Variable a cannot be equal to 0.

$$a=\frac{x}{3x-c}\text{, }a\neq 0$$

Solve for c

$$c=\frac{x\left(3a-1\right)}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$3xa-x=ca$$

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

$$ca=3xa-x$$

The equation is in standard form.

$$ac=3ax-x$$

Divide both sides by a.

$$\frac{ac}{a}=\frac{x\left(3a-1\right)}{a}$$

Dividing by a undoes the multiplication by a.

$$c=\frac{x\left(3a-1\right)}{a}$$