Solve x=frac{x_{1}+rx_{2}}{1+r}

$$x = \frac { x _ { 1 } + r x _ { 2 } } { 1 + r }$$

Solve for r

$$\left\{\begin{matrix}r=-\frac{x-x_{1}}{x-x_{2}}\text{, }&x_{1}\neq x_{2}\text{ and }x\neq x_{2}\\r\neq -1\text{, }&x_{1}=x_{2}\text{ and }x=x_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable r cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by r+1.

$$x\left(r+1\right)=x_{1}+rx_{2}$$

Use the distributive property to multiply x by r+1.

$$xr+x=x_{1}+rx_{2}$$

Subtract rx_{2} from both sides.

$$xr+x-rx_{2}=x_{1}$$

Subtract x from both sides.

$$xr-rx_{2}=x_{1}-x$$

Combine all terms containing r.

$$\left(x-x_{2}\right)r=x_{1}-x$$

Divide both sides by x-x_{2}.

$$\frac{\left(x-x_{2}\right)r}{x-x_{2}}=\frac{x_{1}-x}{x-x_{2}}$$

Dividing by x-x_{2} undoes the multiplication by x-x_{2}.

$$r=\frac{x_{1}-x}{x-x_{2}}$$

Variable r cannot be equal to -1.

$$r=\frac{x_{1}-x}{x-x_{2}}\text{, }r\neq -1$$

Solve for x

$$x=\frac{x_{1}+rx_{2}}{r+1}$$

$$r\neq -1$$