Solve r=-2(-1/3)(2p)+(-1/3)+1/2(3)

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

Solve for p

$$p=\frac{9r+1}{2}$$

Steps for Solving Linear Equation

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

$$r=-\frac{-\frac{2}{3}\times 2p-\frac{1}{3}+1}{2\times 3}$$

Multiply -\frac{2}{3} and 2 to get -\frac{4}{3}.

$$r=-\frac{-\frac{4}{3}p-\frac{1}{3}+1}{2\times 3}$$

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

$$r=-\frac{-\frac{4}{3}p+\frac{2}{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$r=-\frac{-\frac{4}{3}p+\frac{2}{3}}{6}$$

Divide each term of -\frac{4}{3}p+\frac{2}{3} by 6 to get -\frac{2}{9}p+\frac{1}{9}.

$$r=-\left(-\frac{2}{9}p+\frac{1}{9}\right)$$

To find the opposite of -\frac{2}{9}p+\frac{1}{9}, find the opposite of each term.

$$r=\frac{2}{9}p-\frac{1}{9}$$

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

$$\frac{2}{9}p-\frac{1}{9}=r$$

Add \frac{1}{9} to both sides.

$$\frac{2}{9}p=r+\frac{1}{9}$$

Divide both sides of the equation by \frac{2}{9}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{9}p}{\frac{2}{9}}=\frac{r+\frac{1}{9}}{\frac{2}{9}}$$

Dividing by \frac{2}{9} undoes the multiplication by \frac{2}{9}.

$$p=\frac{r+\frac{1}{9}}{\frac{2}{9}}$$

Divide r+\frac{1}{9} by \frac{2}{9} by multiplying r+\frac{1}{9} by the reciprocal of \frac{2}{9}.

$$p=\frac{9r+1}{2}$$

Solve for r

$$r=\frac{2p-1}{9}$$

Solution Steps

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

$$r=-\frac{-\frac{2}{3}\times 2p-\frac{1}{3}+1}{2\times 3}$$

Multiply -\frac{2}{3} and 2 to get -\frac{4}{3}.

$$r=-\frac{-\frac{4}{3}p-\frac{1}{3}+1}{2\times 3}$$

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

$$r=-\frac{-\frac{4}{3}p+\frac{2}{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$r=-\frac{-\frac{4}{3}p+\frac{2}{3}}{6}$$

Divide each term of -\frac{4}{3}p+\frac{2}{3} by 6 to get -\frac{2}{9}p+\frac{1}{9}.

$$r=-\left(-\frac{2}{9}p+\frac{1}{9}\right)$$

To find the opposite of -\frac{2}{9}p+\frac{1}{9}, find the opposite of each term.

$$r=\frac{2}{9}p-\frac{1}{9}$$