Simplify 2/3(27x-45)-(4x-9)

$\frac{2}{3} (27 x - 45) - (4 x - 9)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{2}{3} (27 x) + \frac{2}{3} \cdot - 45 - (4 x - 9)$

Cancel the common factor of $3$ .

Factor $3$ out of $27 x$ .

$\frac{2}{3} (3 (9 x)) + \frac{2}{3} \cdot - 45 - (4 x - 9)$

Cancel the common factor.

$\frac{2}{3} (3 (9 x)) + \frac{2}{3} \cdot - 45 - (4 x - 9)$

Rewrite the expression.

$2 (9 x) + \frac{2}{3} \cdot - 45 - (4 x - 9)$

Multiply $9$ by $2$ .

$18 x + \frac{2}{3} \cdot - 45 - (4 x - 9)$

Cancel the common factor of $3$ .

Factor $3$ out of $- 45$ .

$18 x + \frac{2}{3} \cdot (3 (- 15)) - (4 x - 9)$

Cancel the common factor.

$18 x + \frac{2}{3} \cdot (3 \cdot - 15) - (4 x - 9)$

Rewrite the expression.

$18 x + 2 \cdot - 15 - (4 x - 9)$

Multiply $2$ by $- 15$ .

$18 x - 30 - (4 x - 9)$

Apply the distributive property.

$18 x - 30 - (4 x) - - 9$

Multiply $4$ by $- 1$ .

$18 x - 30 - 4 x - - 9$

Multiply $- 1$ by $- 9$ .

$18 x - 30 - 4 x + 9$

Step 2

Simplify by adding terms.

Subtract $4 x$ from $18 x$ .

$14 x - 30 + 9$

Add $- 30$ and $9$ .

$14 x - 21$