Solve ax-b=bx+5

$$a x - b = b x + 5$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{bx+b+5}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add b to both sides.

$$ax=bx+5+b$$

The equation is in standard form.

$$xa=bx+b+5$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{bx+b+5}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{bx+b+5}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{ax-5}{x+1}\text{, }&x\neq -1\\b\in \mathrm{C}\text{, }&x=-1\text{ and }a=-5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax-b-bx=5$$

Subtract ax from both sides.

$$-b-bx=5-ax$$

Combine all terms containing b.

$$\left(-1-x\right)b=5-ax$$

The equation is in standard form.

$$\left(-x-1\right)b=5-ax$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)b}{-x-1}=\frac{5-ax}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$b=\frac{5-ax}{-x-1}$$

Divide 5-ax by -x-1.

$$b=-\frac{5-ax}{x+1}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{bx+b+5}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add b to both sides.

$$ax=bx+5+b$$

The equation is in standard form.

$$xa=bx+b+5$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{bx+b+5}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{bx+b+5}{x}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ax-5}{x+1}\text{, }&x\neq -1\\b\in \mathrm{R}\text{, }&x=-1\text{ and }a=-5\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$ax-b-bx=5$$

Subtract ax from both sides.

$$-b-bx=5-ax$$

Combine all terms containing b.

$$\left(-1-x\right)b=5-ax$$

The equation is in standard form.

$$\left(-x-1\right)b=5-ax$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)b}{-x-1}=\frac{5-ax}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$b=\frac{5-ax}{-x-1}$$

Divide 5-ax by -x-1.

$$b=-\frac{5-ax}{x+1}$$