Solve for r q-10=6(r+1)

$q - 10 = 6 (r + 1)$

Step 1

Rewrite the equation as $6 (r + 1) = q - 10$ .

$6 (r + 1) = q - 10$

Step 2

Divide each term in $6 (r + 1) = q - 10$ by $6$ and simplify.

Divide each term in $6 (r + 1) = q - 10$ by $6$ .

$\frac{6 (r + 1)}{6} = \frac{q}{6} + \frac{- 10}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 (r + 1)}{6} = \frac{q}{6} + \frac{- 10}{6}$

Divide $r + 1$ by $1$ .

$r + 1 = \frac{q}{6} + \frac{- 10}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 10$ and $6$ .

Factor $2$ out of $- 10$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$r + 1 = \frac{q}{6} + \frac{- 5}{3}$

Move the negative in front of the fraction.

$r + 1 = \frac{q}{6} - \frac{5}{3}$

Step 3

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

Subtract $1$ from both sides of the equation.

$r = \frac{q}{6} - \frac{5}{3} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $- 1$ and $\frac{3}{3}$ .

$r = \frac{q}{6} - \frac{5}{3} + \frac{- 1 \cdot 3}{3}$

Combine the numerators over the common denominator.

$r = \frac{q}{6} + \frac{- 5 - 1 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$r = \frac{q}{6} + \frac{- 5 - 3}{3}$

Subtract $3$ from $- 5$ .

$r = \frac{q}{6} + \frac{- 8}{3}$

Move the negative in front of the fraction.

$r = \frac{q}{6} - \frac{8}{3}$