Solve a=bcx-3ax/4

$$a = \frac { b c x - 3 a x } { 4 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{bcx}{3x+4}\text{, }&x\neq -\frac{4}{3}\\a\in \mathrm{C}\text{, }&\left(b=0\text{ or }c=0\right)\text{ and }x=-\frac{4}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{bcx-3ax}{4} from both sides.

$$a-\frac{bcx-3ax}{4}=0$$

Multiply both sides of the equation by 4.

$$4a-\left(bcx-3ax\right)=0$$

To find the opposite of bcx-3ax, find the opposite of each term.

$$4a-bcx+3ax=0$$

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

$$4a+3ax=bcx$$

Combine all terms containing a.

$$\left(4+3x\right)a=bcx$$

The equation is in standard form.

$$\left(3x+4\right)a=bcx$$

Divide both sides by 4+3x.

$$\frac{\left(3x+4\right)a}{3x+4}=\frac{bcx}{3x+4}$$

Dividing by 4+3x undoes the multiplication by 4+3x.

$$a=\frac{bcx}{3x+4}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{bcx}{3x+4}\text{, }&x\neq -\frac{4}{3}\\a\in \mathrm{R}\text{, }&\left(b=0\text{ or }c=0\right)\text{ and }x=-\frac{4}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{bcx-3ax}{4} from both sides.

$$a-\frac{bcx-3ax}{4}=0$$

Multiply both sides of the equation by 4.

$$4a-\left(bcx-3ax\right)=0$$

To find the opposite of bcx-3ax, find the opposite of each term.

$$4a-bcx+3ax=0$$

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

$$4a+3ax=bcx$$

Combine all terms containing a.

$$\left(4+3x\right)a=bcx$$

The equation is in standard form.

$$\left(3x+4\right)a=bcx$$

Divide both sides by 4+3x.

$$\frac{\left(3x+4\right)a}{3x+4}=\frac{bcx}{3x+4}$$

Dividing by 4+3x undoes the multiplication by 4+3x.

$$a=\frac{bcx}{3x+4}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{a\left(3x+4\right)}{cx}\text{, }&c\neq 0\text{ and }x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(x=-\frac{4}{3}\text{ and }c=0\right)\text{ or }\left(a=0\text{ and }c=0\text{ and }x\neq 0\right)\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a\left(3x+4\right)}{cx}\text{, }&c\neq 0\text{ and }x\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(x=-\frac{4}{3}\text{ and }c=0\right)\text{ or }\left(a=0\text{ and }c=0\text{ and }x\neq 0\right)\end{matrix}\right.$$