Simplify (7r-3/2)-(2/3+6r)

$(7 r - \frac{3}{2}) - (\frac{2}{3} + 6 r)$

Simplify each term.

Apply the distributive property.

$7 r - \frac{3}{2} - \frac{2}{3} - (6 r)$

Multiply $6$ by $- 1$ .

$7 r - \frac{3}{2} - \frac{2}{3} - 6 r$

Subtract $6 r$ from $7 r$ .

$r - \frac{3}{2} - \frac{2}{3}$

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

$r - \frac{3}{2} \cdot \frac{3}{3} - \frac{2}{3}$

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

$r - \frac{3}{2} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{2}{2}$

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

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

$r - \frac{3 \cdot 3}{2 \cdot 3} - \frac{2}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$r - \frac{3 \cdot 3}{6} - \frac{2}{3} \cdot \frac{2}{2}$

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

$r - \frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$r - \frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$r + \frac{- 3 \cdot 3 - 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$r + \frac{- 9 - 2 \cdot 2}{6}$

Multiply $- 2$ by $2$ .

$r + \frac{- 9 - 4}{6}$

Subtract $4$ from $- 9$ .

$r + \frac{- 13}{6}$

Move the negative in front of the fraction.

$r - \frac{13}{6}$