Solve -2(-1/3)=(2(-1/3)+1)/r+2(-frac{1{3})}

$$- 2 ( - \frac { 1 } { 3 } ) = \frac { ( 2 ( - \frac { 1 } { 3 } ) + 1 ) } { r + 2 ( - \frac { 1 } { 3 } ) }$$

Solve for r

$$r = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps for Solving Linear Equation

Multiply -2 and -\frac{1}{3} to get \frac{2}{3}.

$$\frac{2}{3}=\frac{2\left(-\frac{1}{3}\right)+1}{r+2\left(-\frac{1}{3}\right)}$$

Multiply 2 and -\frac{1}{3} to get -\frac{2}{3}.

$$\frac{2}{3}=\frac{-\frac{2}{3}+1}{r+2\left(-\frac{1}{3}\right)}$$

Add -\frac{2}{3} and 1 to get \frac{1}{3}.

$$\frac{2}{3}=\frac{\frac{1}{3}}{r+2\left(-\frac{1}{3}\right)}$$

Multiply 2 and -\frac{1}{3} to get -\frac{2}{3}.

$$\frac{2}{3}=\frac{\frac{1}{3}}{r-\frac{2}{3}}$$

Express \frac{\frac{1}{3}}{r-\frac{2}{3}} as a single fraction.

$$\frac{2}{3}=\frac{1}{3\left(r-\frac{2}{3}\right)}$$

Use the distributive property to multiply 3 by r-\frac{2}{3}.

$$\frac{2}{3}=\frac{1}{3r-2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3r-2}=\frac{2}{3}$$

Variable r cannot be equal to \frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 3\left(3r-2\right), the least common multiple of 3r-2,3.

$$3=2\left(3r-2\right)$$

Divide both sides by 2.

$$\frac{3}{2}=3r-2$$

Swap sides so that all variable terms are on the left hand side.

$$3r-2=\frac{3}{2}$$

Add 2 to both sides.

$$3r=\frac{3}{2}+2$$

Add \frac{3}{2} and 2 to get \frac{7}{2}.

$$3r=\frac{7}{2}$$

Divide both sides by 3.

$$r=\frac{\frac{7}{2}}{3}$$

Express \frac{\frac{7}{2}}{3} as a single fraction.

$$r=\frac{7}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$r=\frac{7}{6}$$