Simplify 2/3(9x-15)-(-6x+2)

$\frac{2}{3} (9 x - 15) - (- 6 x + 2)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{2}{3} (9 x) + \frac{2}{3} \cdot - 15 - (- 6 x + 2)$

Cancel the common factor of $3$ .

Factor $3$ out of $9 x$ .

$\frac{2}{3} (3 (3 x)) + \frac{2}{3} \cdot - 15 - (- 6 x + 2)$

Cancel the common factor.

$\frac{2}{3} (3 (3 x)) + \frac{2}{3} \cdot - 15 - (- 6 x + 2)$

Rewrite the expression.

$2 (3 x) + \frac{2}{3} \cdot - 15 - (- 6 x + 2)$

Multiply $3$ by $2$ .

$6 x + \frac{2}{3} \cdot - 15 - (- 6 x + 2)$

Cancel the common factor of $3$ .

Factor $3$ out of $- 15$ .

$6 x + \frac{2}{3} \cdot (3 (- 5)) - (- 6 x + 2)$

Cancel the common factor.

$6 x + \frac{2}{3} \cdot (3 \cdot - 5) - (- 6 x + 2)$

Rewrite the expression.

$6 x + 2 \cdot - 5 - (- 6 x + 2)$

Multiply $2$ by $- 5$ .

$6 x - 10 - (- 6 x + 2)$

Apply the distributive property.

$6 x - 10 - (- 6 x) - 1 \cdot 2$

Multiply $- 6$ by $- 1$ .

$6 x - 10 + 6 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$6 x - 10 + 6 x - 2$

Step 2

Simplify by adding terms.

Add $6 x$ and $6 x$ .

$12 x - 10 - 2$

Subtract $2$ from $- 10$ .

$12 x - 12$