Solve -ax=b+c

$$- a x = b + c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Reorder the terms.

$$-ax=b+c$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide b+c by -x.

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

Solve for a

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

Steps for Solving Linear Equation

Reorder the terms.

$$-ax=b+c$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide b+c by -x.

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

Solve for b

$$b=-ax-c$$

Solution Steps

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

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

Subtract c from both sides.

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

Reorder the terms.

$$b=-ax-c$$