Solve for b 2/3*(9b-27)=36

$\frac{2}{3} \cdot (9 b - 27) = 36$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (9 b - 27)) = \frac{3}{2} \cdot 36$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (9 b - 27))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} (9 b) + \frac{2}{3} \cdot - 27) = \frac{3}{2} \cdot 36$

Cancel the common factor of $3$ .

Factor $3$ out of $9 b$ .

$\frac{3}{2} (\frac{2}{3} (3 (3 b)) + \frac{2}{3} \cdot - 27) = \frac{3}{2} \cdot 36$

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} (3 (3 b)) + \frac{2}{3} \cdot - 27) = \frac{3}{2} \cdot 36$

Rewrite the expression.

$\frac{3}{2} (2 (3 b) + \frac{2}{3} \cdot - 27) = \frac{3}{2} \cdot 36$

Multiply $3$ by $2$ .

$\frac{3}{2} (6 b + \frac{2}{3} \cdot - 27) = \frac{3}{2} \cdot 36$

Cancel the common factor of $3$ .

Factor $3$ out of $- 27$ .

$\frac{3}{2} (6 b + \frac{2}{3} \cdot (3 (- 9))) = \frac{3}{2} \cdot 36$

Cancel the common factor.

$\frac{3}{2} (6 b + \frac{2}{3} \cdot (3 \cdot - 9)) = \frac{3}{2} \cdot 36$

Rewrite the expression.

$\frac{3}{2} (6 b + 2 \cdot - 9) = \frac{3}{2} \cdot 36$

Multiply $2$ by $- 9$ .

$\frac{3}{2} (6 b - 18) = \frac{3}{2} \cdot 36$

Apply the distributive property.

$\frac{3}{2} (6 b) + \frac{3}{2} \cdot - 18 = \frac{3}{2} \cdot 36$

Cancel the common factor of $2$ .

Factor $2$ out of $6 b$ .

$\frac{3}{2} (2 (3 b)) + \frac{3}{2} \cdot - 18 = \frac{3}{2} \cdot 36$

Cancel the common factor.

$\frac{3}{2} (2 (3 b)) + \frac{3}{2} \cdot - 18 = \frac{3}{2} \cdot 36$

Rewrite the expression.

$3 (3 b) + \frac{3}{2} \cdot - 18 = \frac{3}{2} \cdot 36$

Multiply $3$ by $3$ .

$9 b + \frac{3}{2} \cdot - 18 = \frac{3}{2} \cdot 36$

Cancel the common factor of $2$ .

Factor $2$ out of $- 18$ .

$9 b + \frac{3}{2} \cdot (2 (- 9)) = \frac{3}{2} \cdot 36$

Cancel the common factor.

$9 b + \frac{3}{2} \cdot (2 \cdot - 9) = \frac{3}{2} \cdot 36$

Rewrite the expression.

$9 b + 3 \cdot - 9 = \frac{3}{2} \cdot 36$

Multiply $3$ by $- 9$ .

$9 b - 27 = \frac{3}{2} \cdot 36$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 36$ .

Cancel the common factor of $2$ .

Factor $2$ out of $36$ .

$9 b - 27 = \frac{3}{2} \cdot (2 (18))$

Cancel the common factor.

$9 b - 27 = \frac{3}{2} \cdot (2 \cdot 18)$

Rewrite the expression.

$9 b - 27 = 3 \cdot 18$

Multiply $3$ by $18$ .

$9 b - 27 = 54$

Step 3

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

Add $27$ to both sides of the equation.

$9 b = 54 + 27$

Add $54$ and $27$ .

$9 b = 81$

Step 4

Divide each term in $9 b = 81$ by $9$ and simplify.

Divide each term in $9 b = 81$ by $9$ .

$\frac{9 b}{9} = \frac{81}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 b}{9} = \frac{81}{9}$

Divide $b$ by $1$ .

$b = \frac{81}{9}$

Simplify the right side.

Divide $81$ by $9$ .

$b = 9$

Solve for b 2/3*(9b-27)=36

Related Questions

Support LCMGCF.com by disabling your adblocker.