Solve for r -13=-3/4r

$- 13 = - \frac{3}{4} r$

Step 1

Rewrite the equation as $- \frac{3}{4} r = - 13$ .

$- \frac{3}{4} r = - 13$

Step 2

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

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

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

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

Cancel the common factor of $4$ .

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

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

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

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- r \cdot 3}{4} = - \frac{4}{3} \cdot - 13$

Rewrite the expression.

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

Cancel the common factor of $3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 r = - \frac{4}{3} \cdot - 13$

Multiply $r$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{4}{3} \cdot - 13$ .

Multiply $- 13$ by $- 1$ .

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

Combine $13$ and $\frac{4}{3}$ .

$r = \frac{13 \cdot 4}{3}$

Multiply $13$ by $4$ .

$r = \frac{52}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{52}{3}$

Decimal Form:

$r = 17.\overline{3}$

Mixed Number Form:

$r = 17 \frac{1}{3}$

Solve for r -13=-3/4r

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