Simplify 1/2(2x+4)-1/3(9x-6)

$\frac{1}{2} (2 x + 4) - \frac{1}{3} (9 x - 6)$

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Rewrite the expression.

$x + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x + \frac{1}{2} \cdot (2 (2)) - \frac{1}{3} \cdot (9 x - 6)$

Cancel the common factor.

$x + \frac{1}{2} \cdot (2 \cdot 2) - \frac{1}{3} \cdot (9 x - 6)$

Rewrite the expression.

$x + 2 - \frac{1}{3} \cdot (9 x - 6)$

Apply the distributive property.

$x + 2 - \frac{1}{3} (9 x) - \frac{1}{3} \cdot - 6$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x + 2 + \frac{- 1}{3} (9 x) - \frac{1}{3} \cdot - 6$

Factor $3$ out of $9 x$ .

$x + 2 + \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot - 6$

Cancel the common factor.

$x + 2 + \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot - 6$

Rewrite the expression.

$x + 2 - 1 (3 x) - \frac{1}{3} \cdot - 6$

Multiply $3$ by $- 1$ .

$x + 2 - 3 x - \frac{1}{3} \cdot - 6$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x + 2 - 3 x + \frac{- 1}{3} \cdot - 6$

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x + 2 - 3 x - 1 \cdot - 2$

Multiply $- 1$ by $- 2$ .

$x + 2 - 3 x + 2$

Simplify by adding terms.

Subtract $3 x$ from $x$ .

$- 2 x + 2 + 2$

Add $2$ and $2$ .

$- 2 x + 4$

Simplify 1/2(2x+4)-1/3(9x-6)

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