Solve 7-ax=6x-b

$$7 - a x = 6 x - b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{7+b-6x}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7 from both sides.

$$-ax=6x-b-7$$

The equation is in standard form.

$$\left(-x\right)a=6x-b-7$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{6x-b-7}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{6x-b-7}{-x}$$

Divide 6x-b-7 by -x.

$$a=\frac{b+7}{x}-6$$

Solve for a

$$\left\{\begin{matrix}a=\frac{7+b-6x}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7 from both sides.

$$-ax=6x-b-7$$

The equation is in standard form.

$$\left(-x\right)a=6x-b-7$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{6x-b-7}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$a=\frac{6x-b-7}{-x}$$

Divide 6x-b-7 by -x.

$$a=\frac{b+7}{x}-6$$

Solve for b

$$b=ax+6x-7$$

Steps for Solving Linear Equation

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

$$6x-b=7-ax$$

Subtract 6x from both sides.

$$-b=7-ax-6x$$

The equation is in standard form.

$$-b=7-6x-ax$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{7-6x-ax}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{7-6x-ax}{-1}$$

Divide 7-ax-6x by -1.

$$b=ax+6x-7$$