Simplify x/2-3x+4(x+1)

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

Find the common denominator.

Write $- 3 x$ as a fraction with denominator $1$ .

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

Multiply $\frac{- 3 x}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{- 3 x}{1}$ by $\frac{2}{2}$ .

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

Write $4 (x + 1)$ as a fraction with denominator $1$ .

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

Multiply $\frac{4 (x + 1)}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{4 (x + 1)}{1}$ by $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $2$ by $- 3$ .

$\frac{x - 6 x + 4 (x + 1) \cdot 2}{2}$

Apply the distributive property.

$\frac{x - 6 x + (4 x + 4 \cdot 1) \cdot 2}{2}$

Multiply $4$ by $1$ .

$\frac{x - 6 x + (4 x + 4) \cdot 2}{2}$

Apply the distributive property.

$\frac{x - 6 x + 4 x \cdot 2 + 4 \cdot 2}{2}$

Multiply $2$ by $4$ .

$\frac{x - 6 x + 8 x + 4 \cdot 2}{2}$

Multiply $4$ by $2$ .

$\frac{x - 6 x + 8 x + 8}{2}$

Simplify by adding terms.

Subtract $6 x$ from $x$ .

$\frac{- 5 x + 8 x + 8}{2}$

Add $- 5 x$ and $8 x$ .

$\frac{3 x + 8}{2}$