Solve ax-7b=3ax-c

$$a x - 7 b = 3 a x - c$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{7b-c}{2x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=\frac{c}{7}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3ax from both sides.

$$ax-7b-3ax=-c$$

Combine ax and -3ax to get -2ax.

$$-2ax-7b=-c$$

Add 7b to both sides.

$$-2ax=-c+7b$$

The equation is in standard form.

$$\left(-2x\right)a=7b-c$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)a}{-2x}=\frac{7b-c}{-2x}$$

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

$$a=\frac{7b-c}{-2x}$$

Divide -c+7b by -2x.

$$a=-\frac{7b-c}{2x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{7b-c}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=\frac{c}{7}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3ax from both sides.

$$ax-7b-3ax=-c$$

Combine ax and -3ax to get -2ax.

$$-2ax-7b=-c$$

Add 7b to both sides.

$$-2ax=-c+7b$$

The equation is in standard form.

$$\left(-2x\right)a=7b-c$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)a}{-2x}=\frac{7b-c}{-2x}$$

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

$$a=\frac{7b-c}{-2x}$$

Divide -c+7b by -2x.

$$a=-\frac{7b-c}{2x}$$

Solve for b

$$b=\frac{c-2ax}{7}$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-7b=3ax-c-ax$$

Combine 3ax and -ax to get 2ax.

$$-7b=2ax-c$$

Divide both sides by -7.

$$\frac{-7b}{-7}=\frac{2ax-c}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$b=\frac{2ax-c}{-7}$$

Divide 2ax-c by -7.

$$b=\frac{c-2ax}{7}$$