Simplify 1/3(x+15)+2/3(x+9)

$\frac{1}{3} (x + 15) + \frac{2}{3} (x + 9)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot 15 + \frac{2}{3} \cdot (x + 9)$

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + \frac{1}{3} \cdot 15 + \frac{2}{3} \cdot (x + 9)$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$\frac{x}{3} + \frac{1}{3} \cdot (3 (5)) + \frac{2}{3} \cdot (x + 9)$

Cancel the common factor.

$\frac{x}{3} + \frac{1}{3} \cdot (3 \cdot 5) + \frac{2}{3} \cdot (x + 9)$

Rewrite the expression.

$\frac{x}{3} + 5 + \frac{2}{3} \cdot (x + 9)$

Apply the distributive property.

$\frac{x}{3} + 5 + \frac{2}{3} x + \frac{2}{3} \cdot 9$

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

$\frac{x}{3} + 5 + \frac{2 x}{3} + \frac{2}{3} \cdot 9$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{3} + 5 + \frac{2 x}{3} + 2 \cdot 3$

Multiply $2$ by $3$ .

$\frac{x}{3} + 5 + \frac{2 x}{3} + 6$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$5 + 6 + \frac{x + 2 x}{3}$

Add $x$ and $2 x$ .

$5 + 6 + \frac{3 x}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5 + 6 + \frac{3 x}{3}$

Divide $x$ by $1$ .

$5 + 6 + x$

Add $5$ and $6$ .

$11 + x$