Simplify 7-(x-3)/4+2

$7 - \frac{x - 3}{4} + 2$

Find the common denominator.

Write $7$ as a fraction with denominator $1$ .

$\frac{7}{1} - \frac{x - 3}{4} + 2$

Multiply $\frac{7}{1}$ by $\frac{4}{4}$ .

$\frac{7}{1} \cdot \frac{4}{4} - \frac{x - 3}{4} + 2$

Multiply $\frac{7}{1}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 4}{4} - \frac{x - 3}{4} + 2$

Write $2$ as a fraction with denominator $1$ .

$\frac{7 \cdot 4}{4} - \frac{x - 3}{4} + \frac{2}{1}$

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 4}{4} - \frac{x - 3}{4} + \frac{2}{1} \cdot \frac{4}{4}$

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 4}{4} - \frac{x - 3}{4} + \frac{2 \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 - (x - 3) + 2 \cdot 4}{4}$

Simplify each term.

Multiply $7$ by $4$ .

$\frac{28 - (x - 3) + 2 \cdot 4}{4}$

Apply the distributive property.

$\frac{28 - x - - 3 + 2 \cdot 4}{4}$

Multiply $- 1$ by $- 3$ .

$\frac{28 - x + 3 + 2 \cdot 4}{4}$

Multiply $2$ by $4$ .

$\frac{28 - x + 3 + 8}{4}$

Simplify with factoring out.

Add $28$ and $3$ .

$\frac{- x + 31 + 8}{4}$

Add $31$ and $8$ .

$\frac{- x + 39}{4}$

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 39}{4}$

Rewrite $39$ as $- 1 (- 39)$ .

$\frac{- (x) - 1 (- 39)}{4}$

Factor $- 1$ out of $- (x) - 1 (- 39)$ .

$\frac{- (x - 39)}{4}$

Simplify the expression.

Rewrite $- (x - 39)$ as $- 1 (x - 39)$ .

$\frac{- 1 (x - 39)}{4}$

Move the negative in front of the fraction.

$- \frac{x - 39}{4}$