Solve -(a+b)c=-a-b

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

Solve for a

$$\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&c=1\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of a+b, find the opposite of each term.

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

Use the distributive property to multiply -a-b by c.

$$-ac-bc=-a-b$$

Add a to both sides.

$$-ac-bc+a=-b$$

Add bc to both sides.

$$-ac+a=-b+bc$$

Combine all terms containing a.

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

The equation is in standard form.

$$\left(1-c\right)a=bc-b$$

Divide both sides by 1-c.

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

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

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

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

$$a=-b$$

Solve for b

$$\left\{\begin{matrix}\\b=-a\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&c=1\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of a+b, find the opposite of each term.

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

Use the distributive property to multiply -a-b by c.

$$-ac-bc=-a-b$$

Add b to both sides.

$$-ac-bc+b=-a$$

Add ac to both sides.

$$-bc+b=-a+ac$$

Combine all terms containing b.

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

The equation is in standard form.

$$\left(1-c\right)b=ac-a$$

Divide both sides by 1-c.

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

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

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

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

$$b=-a$$