Solve for b 2/3(b+9)=6+2(b-6)

$\frac{2}{3} (b + 9) = 6 + 2 (b - 6)$

Step 1

Simplify $\frac{2}{3} \cdot (b + 9)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (b + 9) = 6 + 2 (b - 6)$

Simplify by adding zeros.

$\frac{2}{3} \cdot (b + 9) = 6 + 2 (b - 6)$

Apply the distributive property.

$\frac{2}{3} b + \frac{2}{3} \cdot 9 = 6 + 2 (b - 6)$

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

$\frac{2 b}{3} + \frac{2}{3} \cdot 9 = 6 + 2 (b - 6)$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{2 b}{3} + \frac{2}{3} \cdot (3 (3)) = 6 + 2 (b - 6)$

Cancel the common factor.

$\frac{2 b}{3} + \frac{2}{3} \cdot (3 \cdot 3) = 6 + 2 (b - 6)$

Rewrite the expression.

$\frac{2 b}{3} + 2 \cdot 3 = 6 + 2 (b - 6)$

Multiply $2$ by $3$ .

$\frac{2 b}{3} + 6 = 6 + 2 (b - 6)$

Step 2

Simplify $6 + 2 (b - 6)$ .

Simplify each term.

Apply the distributive property.

$\frac{2 b}{3} + 6 = 6 + 2 b + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$\frac{2 b}{3} + 6 = 6 + 2 b - 12$

Subtract $12$ from $6$ .

$\frac{2 b}{3} + 6 = 2 b - 6$

Step 3

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

Subtract $2 b$ from both sides of the equation.

$\frac{2 b}{3} + 6 - 2 b = - 6$

To write $- 2 b$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 b}{3} - 2 b \cdot \frac{3}{3} + 6 = - 6$

Combine $- 2 b$ and $\frac{3}{3}$ .

$\frac{2 b}{3} + \frac{- 2 b \cdot 3}{3} + 6 = - 6$

Combine the numerators over the common denominator.

$\frac{2 b - 2 b \cdot 3}{3} + 6 = - 6$

Simplify each term.

Simplify the numerator.

Factor $2 b$ out of $2 b - 2 b \cdot 3$ .

Factor $2 b$ out of $2 b$ .

$\frac{2 b (1) - 2 b \cdot 3}{3} + 6 = - 6$

Factor $2 b$ out of $- 2 b \cdot 3$ .

$\frac{2 b (1) + 2 b (- 1 \cdot 3)}{3} + 6 = - 6$

Factor $2 b$ out of $2 b (1) + 2 b (- 1 \cdot 3)$ .

$\frac{2 b (1 - 1 \cdot 3)}{3} + 6 = - 6$

Multiply $- 1$ by $3$ .

$\frac{2 b (1 - 3)}{3} + 6 = - 6$

Subtract $3$ from $1$ .

$\frac{2 b \cdot - 2}{3} + 6 = - 6$

Multiply $- 2$ by $2$ .

$\frac{- 4 b}{3} + 6 = - 6$

Move the negative in front of the fraction.

$- \frac{4 b}{3} + 6 = - 6$

Step 4

Move all terms not containing $b$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$- \frac{4 b}{3} = - 6 - 6$

Subtract $6$ from $- 6$ .

$- \frac{4 b}{3} = - 12$

Step 5

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 b}{3}) = - \frac{3}{4} \cdot - 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{4} (- \frac{4 b}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 b}{3}) = - \frac{3}{4} \cdot - 12$

Move the leading negative in $- \frac{4 b}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 b}{3} = - \frac{3}{4} \cdot - 12$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 b}{3} = - \frac{3}{4} \cdot - 12$

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 b}{3} = - \frac{3}{4} \cdot - 12$

Rewrite the expression.

$\frac{- 1}{4} (- 4 b) = - \frac{3}{4} \cdot - 12$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 b$ .

$\frac{- 1}{4} (4 (- b)) = - \frac{3}{4} \cdot - 12$

Cancel the common factor.

$\frac{- 1}{4} (4 (- b)) = - \frac{3}{4} \cdot - 12$

Rewrite the expression.

$- - b = - \frac{3}{4} \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{3}{4} \cdot - 12$

Multiply $b$ by $1$ .

$b = - \frac{3}{4} \cdot - 12$

Simplify the right side.

Simplify $- \frac{3}{4} \cdot - 12$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$b = \frac{- 3}{4} \cdot - 12$

Factor $4$ out of $- 12$ .

$b = \frac{- 3}{4} \cdot (4 (- 3))$

Cancel the common factor.

$b = \frac{- 3}{4} \cdot (4 \cdot - 3)$

Rewrite the expression.

$b = - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$b = 9$

Solve for b 2/3(b+9)=6+2(b-6)

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