Solve (c)a-b=b-a

$$( c ) a - b = b - a$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2b}{c+1}\text{, }&c\neq -1\\a\in \mathrm{R}\text{, }&b=0\text{ and }c=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a to both sides.

$$ca-b+a=b$$

Add b to both sides.

$$ca+a=b+b$$

Combine b and b to get 2b.

$$ca+a=2b$$

Combine all terms containing a.

$$\left(c+1\right)a=2b$$

Divide both sides by c+1.

$$\frac{\left(c+1\right)a}{c+1}=\frac{2b}{c+1}$$

Dividing by c+1 undoes the multiplication by c+1.

$$a=\frac{2b}{c+1}$$

Solve for b

$$b=\frac{a\left(c+1\right)}{2}$$

Steps for Solving Linear Equation

Subtract b from both sides.

$$ca-b-b=-a$$

Combine -b and -b to get -2b.

$$ca-2b=-a$$

Subtract ca from both sides.

$$-2b=-a-ca$$

The equation is in standard form.

$$-2b=-ac-a$$

Divide both sides by -2.

$$\frac{-2b}{-2}=-\frac{a\left(c+1\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$b=-\frac{a\left(c+1\right)}{-2}$$

Divide -a\left(1+c\right) by -2.

$$b=\frac{a\left(c+1\right)}{2}$$