Solve -ax+bx=c

$$- a x + b x = c$$

Solve for a

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

Steps for Solving Linear Equation

Subtract bx from both sides.

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

Reorder the terms.

$$-ax=-bx+c$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide c-bx by -x.

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

Solve for b

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

Steps for Solving Linear Equation

Subtract \left(-a\right)x from both sides.

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

Multiply -1 and -1 to get 1.

$$bx=c+ax$$

The equation is in standard form.

$$xb=ax+c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ax+c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ax+c}{x}$$

Divide c+ax by x.

$$b=a+\frac{c}{x}$$