Solve for a 1/3(6+3a)=3a

$\frac{1}{3} (6 + 3 a) = 3 a$

Step 1

Simplify $\frac{1}{3} \cdot (6 + 3 a)$ .

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (6 + 3 a) = 3 a$

Simplify by adding zeros.

$\frac{1}{3} \cdot (6 + 3 a) = 3 a$

Apply the distributive property.

$\frac{1}{3} \cdot 6 + \frac{1}{3} (3 a) = 3 a$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{1}{3} \cdot (3 (2)) + \frac{1}{3} (3 a) = 3 a$

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 2) + \frac{1}{3} (3 a) = 3 a$

Rewrite the expression.

$2 + \frac{1}{3} (3 a) = 3 a$

Cancel the common factor of $3$ .

Factor $3$ out of $3 a$ .

$2 + \frac{1}{3} (3 (a)) = 3 a$

Cancel the common factor.

$2 + \frac{1}{3} (3 a) = 3 a$

Rewrite the expression.

$2 + a = 3 a$

Step 2

Move all terms containing $a$ to the left side of the equation.

Subtract $3 a$ from both sides of the equation.

$2 + a - 3 a = 0$

Subtract $3 a$ from $a$ .

$2 - 2 a = 0$

Step 3

Subtract $2$ from both sides of the equation.

$- 2 a = - 2$

Step 4

Divide each term in $- 2 a = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 a = - 2$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 2}{- 2}$

Divide $a$ by $1$ .

$a = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$a = 1$