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

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply -a+b by x.

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

Subtract a from both sides.

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

Subtract bx from both sides.

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

Reorder the terms.

$$-ax-a=-bx-b$$

Combine all terms containing a.

$$\left(-x-1\right)a=-bx-b$$

Divide both sides by -1-x.

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

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

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

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

$$a=b$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply -a+b by x.

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

Add b to both sides.

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

Subtract \left(-a\right)x from both sides.

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

Multiply -1 and -1 to get 1.

$$bx+b=a+ax$$

Combine all terms containing b.

$$\left(x+1\right)b=a+ax$$

The equation is in standard form.

$$\left(x+1\right)b=ax+a$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)b}{x+1}=\frac{ax+a}{x+1}$$

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

$$b=\frac{ax+a}{x+1}$$

Divide a+ax by x+1.

$$b=a$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply -a+b by x.

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

Subtract a from both sides.

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

Subtract bx from both sides.

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

Reorder the terms.

$$-ax-a=-bx-b$$

Combine all terms containing a.

$$\left(-x-1\right)a=-bx-b$$

Divide both sides by -1-x.

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

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

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

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

$$a=b$$

Solve for b

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

Steps for Solving Linear Equation

Use the distributive property to multiply -a+b by x.

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

Add b to both sides.

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

Subtract \left(-a\right)x from both sides.

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

Multiply -1 and -1 to get 1.

$$bx+b=a+ax$$

Combine all terms containing b.

$$\left(x+1\right)b=a+ax$$

The equation is in standard form.

$$\left(x+1\right)b=ax+a$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)b}{x+1}=\frac{ax+a}{x+1}$$

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

$$b=\frac{ax+a}{x+1}$$

Divide a+ax by x+1.

$$b=a$$