Solve for r 1+r/-1.5=9

$1 + \frac{r}{- 1.5} = 9$

Simplify each term.

Move the negative in front of the fraction.

$1 - \frac{r}{1.5} = 9$

Multiply by $1$ .

$1 - \frac{1 r}{1.5} = 9$

Factor $1.5$ out of $1.5$ .

$1 - \frac{1 r}{1.5 (1)} = 9$

Separate fractions.

$1 - (\frac{1}{1.5} \cdot \frac{r}{1}) = 9$

Divide $1$ by $1.5$ .

$1 - (0.\overline{6} \frac{r}{1}) = 9$

Divide $r$ by $1$ .

$1 - (0.\overline{6} r) = 9$

Multiply $0.\overline{6}$ by $- 1$ .

$1 - 0.\overline{6} r = 9$

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

Subtract $1$ from both sides of the equation.

$- 0.\overline{6} r = 9 - 1$

Subtract $1$ from $9$ .

$- 0.\overline{6} r = 8$

Divide each term in $- 0.\overline{6} r = 8$ by $- 0.\overline{6}$ and simplify.

Divide each term in $- 0.\overline{6} r = 8$ by $- 0.\overline{6}$ .

$\frac{- 0.\overline{6} r}{- 0.\overline{6}} = \frac{8}{- 0.\overline{6}}$

Simplify the left side.

Cancel the common factor of $- 0.\overline{6}$ .

Cancel the common factor.

$\frac{- 0.\overline{6} r}{- 0.\overline{6}} = \frac{8}{- 0.\overline{6}}$

Divide $r$ by $1$ .

$r = \frac{8}{- 0.\overline{6}}$

Simplify the right side.

Divide $8$ by $- 0.\overline{6}$ .

$r = - 12$