Simplify 1/3(9-6m)+1/4(12m-8)

$\frac{1}{3} (9 - 6 m) + \frac{1}{4} (12 m - 8)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{3} \cdot 9 + \frac{1}{3} (- 6 m) + \frac{1}{4} \cdot (12 m - 8)$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{1}{3} \cdot (3 (3)) + \frac{1}{3} (- 6 m) + \frac{1}{4} \cdot (12 m - 8)$

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 3) + \frac{1}{3} (- 6 m) + \frac{1}{4} \cdot (12 m - 8)$

Rewrite the expression.

$3 + \frac{1}{3} (- 6 m) + \frac{1}{4} \cdot (12 m - 8)$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6 m$ .

$3 + \frac{1}{3} (3 (- 2 m)) + \frac{1}{4} \cdot (12 m - 8)$

Cancel the common factor.

$3 + \frac{1}{3} (3 (- 2 m)) + \frac{1}{4} \cdot (12 m - 8)$

Rewrite the expression.

$3 - 2 m + \frac{1}{4} \cdot (12 m - 8)$

Apply the distributive property.

$3 - 2 m + \frac{1}{4} (12 m) + \frac{1}{4} \cdot - 8$

Cancel the common factor of $4$ .

Factor $4$ out of $12 m$ .

$3 - 2 m + \frac{1}{4} (4 (3 m)) + \frac{1}{4} \cdot - 8$

Cancel the common factor.

$3 - 2 m + \frac{1}{4} (4 (3 m)) + \frac{1}{4} \cdot - 8$

Rewrite the expression.

$3 - 2 m + 3 m + \frac{1}{4} \cdot - 8$

Cancel the common factor of $4$ .

Factor $4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 - 2 m + 3 m - 2$

Step 2

Simplify by adding terms.

Subtract $2$ from $3$ .

$- 2 m + 3 m + 1$

Add $- 2 m$ and $3 m$ .

$m + 1$