Solve x:(3a-1)x=b

$$x : ( 3 a - 1 ) x = b$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{2}+b}{3b}\text{, }&x\neq 0\text{ and }b\neq 0\\a\neq \frac{1}{3}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3a-1.

$$xx=b\left(3a-1\right)$$

Multiply x and x to get x^{2}.

$$x^{2}=b\left(3a-1\right)$$

Use the distributive property to multiply b by 3a-1.

$$x^{2}=3ba-b$$

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

$$3ba-b=x^{2}$$

Add b to both sides.

$$3ba=x^{2}+b$$

Divide both sides by 3b.

$$\frac{3ba}{3b}=\frac{x^{2}+b}{3b}$$

Dividing by 3b undoes the multiplication by 3b.

$$a=\frac{x^{2}+b}{3b}$$

Variable a cannot be equal to \frac{1}{3}.

$$a=\frac{x^{2}+b}{3b}\text{, }a\neq \frac{1}{3}$$

Solve for b

$$b=-\frac{x^{2}}{1-3a}$$

$$a\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3a-1.

$$xx=b\left(3a-1\right)$$

Multiply x and x to get x^{2}.

$$x^{2}=b\left(3a-1\right)$$

Use the distributive property to multiply b by 3a-1.

$$x^{2}=3ba-b$$

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

$$3ba-b=x^{2}$$

Combine all terms containing b.

$$\left(3a-1\right)b=x^{2}$$

Divide both sides by 3a-1.

$$\frac{\left(3a-1\right)b}{3a-1}=\frac{x^{2}}{3a-1}$$

Dividing by 3a-1 undoes the multiplication by 3a-1.

$$b=\frac{x^{2}}{3a-1}$$