Solve for r -r+3-1/9r=2r+1-8/9r

$- r + 3 - \frac{1}{9} r = 2 r + 1 - \frac{8}{9} r$

Simplify $- r + 3 - \frac{1}{9} r$ .

Combine $r$ and $\frac{1}{9}$ .

$- r + 3 - \frac{r}{9} = 2 r + 1 - \frac{8}{9} r$

To write $- r$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- r \cdot \frac{9}{9} - \frac{r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Simplify terms.

Combine $- r$ and $\frac{9}{9}$ .

$\frac{- r \cdot 9}{9} - \frac{r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Combine the numerators over the common denominator.

$\frac{- r \cdot 9 - r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Simplify each term.

Simplify the numerator.

Factor $r$ out of $- r \cdot 9 - r$ .

Factor $r$ out of $- r \cdot 9$ .

$\frac{r (- 1 \cdot 9) - r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Factor $r$ out of $- r$ .

$\frac{r (- 1 \cdot 9) + r \cdot - 1}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Factor $r$ out of $r (- 1 \cdot 9) + r \cdot - 1$ .

$\frac{r (- 1 \cdot 9 - 1)}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Multiply $- 1$ by $9$ .

$\frac{r (- 9 - 1)}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Subtract $1$ from $- 9$ .

$\frac{r \cdot - 10}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Move $- 10$ to the left of $r$ .

$\frac{- 10 \cdot r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Move the negative in front of the fraction.

$- \frac{10 r}{9} + 3 = 2 r + 1 - \frac{8}{9} r$

Simplify $2 r + 1 - \frac{8}{9} r$ .

Simplify each term.

Combine $r$ and $\frac{8}{9}$ .

$- \frac{10 r}{9} + 3 = 2 r + 1 - \frac{r \cdot 8}{9}$

Move $8$ to the left of $r$ .

$- \frac{10 r}{9} + 3 = 2 r + 1 - \frac{8 r}{9}$

To write $2 r$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{10 r}{9} + 3 = 2 r \cdot \frac{9}{9} - \frac{8 r}{9} + 1$

Simplify terms.

Combine $2 r$ and $\frac{9}{9}$ .

$- \frac{10 r}{9} + 3 = \frac{2 r \cdot 9}{9} - \frac{8 r}{9} + 1$

Combine the numerators over the common denominator.

$- \frac{10 r}{9} + 3 = \frac{2 r \cdot 9 - 8 r}{9} + 1$

Simplify the numerator.

Factor $2 r$ out of $2 r \cdot 9 - 8 r$ .

Factor $2 r$ out of $2 r \cdot 9$ .

$- \frac{10 r}{9} + 3 = \frac{2 r (9) - 8 r}{9} + 1$

Factor $2 r$ out of $- 8 r$ .

$- \frac{10 r}{9} + 3 = \frac{2 r (9) + 2 r (- 4)}{9} + 1$

Factor $2 r$ out of $2 r (9) + 2 r (- 4)$ .

$- \frac{10 r}{9} + 3 = \frac{2 r (9 - 4)}{9} + 1$

Subtract $4$ from $9$ .

$- \frac{10 r}{9} + 3 = \frac{2 r \cdot 5}{9} + 1$

Multiply $5$ by $2$ .

$- \frac{10 r}{9} + 3 = \frac{10 r}{9} + 1$

Move all terms containing $r$ to the left side of the equation.

Subtract $\frac{10 r}{9}$ from both sides of the equation.

$- \frac{10 r}{9} + 3 - \frac{10 r}{9} = 1$

Combine the numerators over the common denominator.

$3 + \frac{- 10 r - 10 r}{9} = 1$

Subtract $10 r$ from $- 10 r$ .

$3 + \frac{- 20 r}{9} = 1$

Move the negative in front of the fraction.

$3 - \frac{20 r}{9} = 1$

Move all terms not containing $r$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$- \frac{20 r}{9} = 1 - 3$

Subtract $3$ from $1$ .

$- \frac{20 r}{9} = - 2$

Multiply both sides of the equation by $- \frac{9}{20}$ .

$- \frac{9}{20} (- \frac{20 r}{9}) = - \frac{9}{20} \cdot - 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{9}{20} (- \frac{20 r}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{9}{20}$ into the numerator.

$\frac{- 9}{20} (- \frac{20 r}{9}) = - \frac{9}{20} \cdot - 2$

Move the leading negative in $- \frac{20 r}{9}$ into the numerator.

$\frac{- 9}{20} \cdot \frac{- 20 r}{9} = - \frac{9}{20} \cdot - 2$

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{20} \cdot \frac{- 20 r}{9} = - \frac{9}{20} \cdot - 2$

Cancel the common factor.

$\frac{9 \cdot - 1}{20} \cdot \frac{- 20 r}{9} = - \frac{9}{20} \cdot - 2$

Rewrite the expression.

$\frac{- 1}{20} (- 20 r) = - \frac{9}{20} \cdot - 2$

Cancel the common factor of $20$ .

Factor $20$ out of $- 20 r$ .

$\frac{- 1}{20} (20 (- r)) = - \frac{9}{20} \cdot - 2$

Cancel the common factor.

$\frac{- 1}{20} (20 (- r)) = - \frac{9}{20} \cdot - 2$

Rewrite the expression.

$- - r = - \frac{9}{20} \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 r = - \frac{9}{20} \cdot - 2$

Multiply $r$ by $1$ .

$r = - \frac{9}{20} \cdot - 2$

Simplify the right side.

Simplify $- \frac{9}{20} \cdot - 2$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9}{20}$ into the numerator.

$r = \frac{- 9}{20} \cdot - 2$

Factor $2$ out of $20$ .

$r = \frac{- 9}{2 (10)} \cdot - 2$

Factor $2$ out of $- 2$ .

$r = \frac{- 9}{2 \cdot 10} \cdot (2 \cdot - 1)$

Cancel the common factor.

$r = \frac{- 9}{2 \cdot 10} \cdot (2 \cdot - 1)$

Rewrite the expression.

$r = \frac{- 9}{10} \cdot - 1$

Combine $\frac{- 9}{10}$ and $- 1$ .

$r = \frac{- 9 \cdot - 1}{10}$

Multiply $- 9$ by $- 1$ .

$r = \frac{9}{10}$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{9}{10}$

Decimal Form:

$r = 0.9$

Solve for r -r+3-1/9r=2r+1-8/9r

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