Solve x/a+b=c

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

Solve for a

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

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$x+ab=ca$$

Subtract ca from both sides.

$$x+ab-ca=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$ab-ca=-x$$

Combine all terms containing a.

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

Divide both sides by b-c.

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

Dividing by b-c undoes the multiplication by b-c.

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

Variable a cannot be equal to 0.

$$a=-\frac{x}{b-c}\text{, }a\neq 0$$

Solve for b

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

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$x+ab=ca$$

Subtract x from both sides.

$$ab=ca-x$$

The equation is in standard form.

$$ab=ac-x$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{ac-x}{a}$$

Dividing by a undoes the multiplication by a.

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

Divide ca-x by a.

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