Solve for r 5/6r-3(r+3)-1/2r=-4/3r

$\frac{5}{6} r - 3 (r + 3) - \frac{1}{2} r = - \frac{4}{3} r$

Simplify $\frac{5}{6} r - 3 (r + 3) - \frac{1}{2} r$ .

Simplify each term.

Combine $\frac{5}{6}$ and $r$ .

$\frac{5 r}{6} - 3 (r + 3) - \frac{1}{2} r = - \frac{4}{3} r$

Apply the distributive property.

$\frac{5 r}{6} - 3 r - 3 \cdot 3 - \frac{1}{2} r = - \frac{4}{3} r$

Multiply $- 3$ by $3$ .

$\frac{5 r}{6} - 3 r - 9 - \frac{1}{2} r = - \frac{4}{3} r$

Combine $r$ and $\frac{1}{2}$ .

$\frac{5 r}{6} - 3 r - 9 - \frac{r}{2} = - \frac{4}{3} r$

To write $- 3 r$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 r}{6} - 3 r \cdot \frac{6}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Simplify terms.

Combine $- 3 r$ and $\frac{6}{6}$ .

$\frac{5 r}{6} + \frac{- 3 r \cdot 6}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Combine the numerators over the common denominator.

$\frac{5 r - 3 r \cdot 6}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Simplify each term.

Simplify the numerator.

Factor $r$ out of $5 r - 3 r \cdot 6$ .

Factor $r$ out of $5 r$ .

$\frac{r \cdot 5 - 3 r \cdot 6}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Factor $r$ out of $- 3 r \cdot 6$ .

$\frac{r \cdot 5 + r (- 3 \cdot 6)}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Factor $r$ out of $r \cdot 5 + r (- 3 \cdot 6)$ .

$\frac{r (5 - 3 \cdot 6)}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Multiply $- 3$ by $6$ .

$\frac{r (5 - 18)}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Subtract $18$ from $5$ .

$\frac{r \cdot - 13}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Move $- 13$ to the left of $r$ .

$\frac{- 13 \cdot r}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

Move the negative in front of the fraction.

$- \frac{13 r}{6} - 9 - \frac{r}{2} = - \frac{4}{3} r$

To write $- \frac{r}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{13 r}{6} - \frac{r}{2} \cdot \frac{3}{3} - 9 = - \frac{4}{3} r$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{r}{2}$ by $\frac{3}{3}$ .

$- \frac{13 r}{6} - \frac{r \cdot 3}{2 \cdot 3} - 9 = - \frac{4}{3} r$

Multiply $2$ by $3$ .

$- \frac{13 r}{6} - \frac{r \cdot 3}{6} - 9 = - \frac{4}{3} r$

Combine the numerators over the common denominator.

$\frac{- 13 r - r \cdot 3}{6} - 9 = - \frac{4}{3} r$

Simplify each term.

Simplify the numerator.

Factor $r$ out of $- 13 r - r \cdot 3$ .

Factor $r$ out of $- 13 r$ .

$\frac{r \cdot - 13 - r \cdot 3}{6} - 9 = - \frac{4}{3} r$

Factor $r$ out of $- r \cdot 3$ .

$\frac{r \cdot - 13 + r (- 1 \cdot 3)}{6} - 9 = - \frac{4}{3} r$

Factor $r$ out of $r \cdot - 13 + r (- 1 \cdot 3)$ .

$\frac{r (- 13 - 1 \cdot 3)}{6} - 9 = - \frac{4}{3} r$

Multiply $- 1$ by $3$ .

$\frac{r (- 13 - 3)}{6} - 9 = - \frac{4}{3} r$

Subtract $3$ from $- 13$ .

$\frac{r \cdot - 16}{6} - 9 = - \frac{4}{3} r$

Cancel the common factor of $- 16$ and $6$ .

Factor $2$ out of $r \cdot - 16$ .

$\frac{2 (r \cdot - 8)}{6} - 9 = - \frac{4}{3} r$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 (r \cdot - 8)}{2 (3)} - 9 = - \frac{4}{3} r$

Cancel the common factor.

$\frac{2 (r \cdot - 8)}{2 \cdot 3} - 9 = - \frac{4}{3} r$

Rewrite the expression.

$\frac{r \cdot - 8}{3} - 9 = - \frac{4}{3} r$

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

$\frac{- 8 \cdot r}{3} - 9 = - \frac{4}{3} r$

Move the negative in front of the fraction.

$- \frac{8 r}{3} - 9 = - \frac{4}{3} r$

Simplify $- \frac{4}{3} r$ .

Combine $r$ and $\frac{4}{3}$ .

$- \frac{8 r}{3} - 9 = - \frac{r \cdot 4}{3}$

Move $4$ to the left of $r$ .

$- \frac{8 r}{3} - 9 = - \frac{4 r}{3}$

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

Add $\frac{4 r}{3}$ to both sides of the equation.

$- \frac{8 r}{3} - 9 + \frac{4 r}{3} = 0$

Combine the numerators over the common denominator.

$- 9 + \frac{- 8 r + 4 r}{3} = 0$

Add $- 8 r$ and $4 r$ .

$- 9 + \frac{- 4 r}{3} = 0$

Move the negative in front of the fraction.

$- 9 - \frac{4 r}{3} = 0$

Add $9$ to both sides of the equation.

$- \frac{4 r}{3} = 9$

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 r}{3}) = - \frac{3}{4} \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{4} (- \frac{4 r}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 r}{3}) = - \frac{3}{4} \cdot 9$

Move the leading negative in $- \frac{4 r}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 r}{3} = - \frac{3}{4} \cdot 9$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 r}{3} = - \frac{3}{4} \cdot 9$

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 r}{3} = - \frac{3}{4} \cdot 9$

Rewrite the expression.

$\frac{- 1}{4} (- 4 r) = - \frac{3}{4} \cdot 9$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 r$ .

$\frac{- 1}{4} (4 (- r)) = - \frac{3}{4} \cdot 9$

Cancel the common factor.

$\frac{- 1}{4} (4 (- r)) = - \frac{3}{4} \cdot 9$

Rewrite the expression.

$- - r = - \frac{3}{4} \cdot 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 r = - \frac{3}{4} \cdot 9$

Multiply $r$ by $1$ .

$r = - \frac{3}{4} \cdot 9$

Simplify the right side.

Simplify $- \frac{3}{4} \cdot 9$ .

Multiply $- \frac{3}{4} \cdot 9$ .

Multiply $9$ by $- 1$ .

$r = - 9 (\frac{3}{4})$

Combine $- 9$ and $\frac{3}{4}$ .

$r = \frac{- 9 \cdot 3}{4}$

Multiply $- 9$ by $3$ .

$r = \frac{- 27}{4}$

Move the negative in front of the fraction.

$r = - \frac{27}{4}$

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{27}{4}$

Decimal Form:

$r = - 6.75$

Mixed Number Form:

$r = - 6 \frac{3}{4}$

Solve for r 5/6r-3(r+3)-1/2r=-4/3r

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