Simplify -1/2(b+2)+3b

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

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} b - \frac{1}{2} \cdot 2 + 3 b$

Combine $b$ and $\frac{1}{2}$ .

$- \frac{b}{2} - \frac{1}{2} \cdot 2 + 3 b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- \frac{b}{2} + \frac{- 1}{2} \cdot 2 + 3 b$

Cancel the common factor.

$- \frac{b}{2} + \frac{- 1}{2} \cdot 2 + 3 b$

Rewrite the expression.

$- \frac{b}{2} - 1 + 3 b$

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

$- \frac{b}{2} + 3 b \cdot \frac{2}{2} - 1$

Simplify terms.

Combine $3 b$ and $\frac{2}{2}$ .

$- \frac{b}{2} + \frac{3 b \cdot 2}{2} - 1$

Combine the numerators over the common denominator.

$\frac{- b + 3 b \cdot 2}{2} - 1$

Simplify each term.

Simplify the numerator.

Factor $b$ out of $- b + 3 b \cdot 2$ .

Factor $b$ out of $- b$ .

$\frac{b \cdot - 1 + 3 b \cdot 2}{2} - 1$

Factor $b$ out of $3 b \cdot 2$ .

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

Factor $b$ out of $b \cdot - 1 + b (3 \cdot 2)$ .

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

Multiply $3$ by $2$ .

$\frac{b (- 1 + 6)}{2} - 1$

Add $- 1$ and $6$ .

$\frac{b \cdot 5}{2} - 1$

Move $5$ to the left of $b$ .

$\frac{5 b}{2} - 1$