Solve for v 8/9(1/2v-18)+2v=2/3v

$\frac{8}{9} (\frac{1}{2} v - 18) + 2 v = \frac{2}{3} v$

Simplify $\frac{8}{9} \cdot (\frac{1}{2} v - 18) + 2 v$ .

Simplify each term.

Combine $\frac{1}{2}$ and $v$ .

$\frac{8}{9} \cdot (\frac{v}{2} - 18) + 2 v = \frac{2}{3} v$

Apply the distributive property.

$\frac{8}{9} \cdot \frac{v}{2} + \frac{8}{9} \cdot - 18 + 2 v = \frac{2}{3} v$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{9} \cdot \frac{v}{2} + \frac{8}{9} \cdot - 18 + 2 v = \frac{2}{3} v$

Cancel the common factor.

$\frac{2 \cdot 4}{9} \cdot \frac{v}{2} + \frac{8}{9} \cdot - 18 + 2 v = \frac{2}{3} v$

Rewrite the expression.

$\frac{4}{9} v + \frac{8}{9} \cdot - 18 + 2 v = \frac{2}{3} v$

Combine $\frac{4}{9}$ and $v$ .

$\frac{4 v}{9} + \frac{8}{9} \cdot - 18 + 2 v = \frac{2}{3} v$

Cancel the common factor of $9$ .

Factor $9$ out of $- 18$ .

$\frac{4 v}{9} + \frac{8}{9} \cdot (9 (- 2)) + 2 v = \frac{2}{3} v$

Cancel the common factor.

$\frac{4 v}{9} + \frac{8}{9} \cdot (9 \cdot - 2) + 2 v = \frac{2}{3} v$

Rewrite the expression.

$\frac{4 v}{9} + 8 \cdot - 2 + 2 v = \frac{2}{3} v$

Multiply $8$ by $- 2$ .

$\frac{4 v}{9} - 16 + 2 v = \frac{2}{3} v$

To write $2 v$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4 v}{9} + 2 v \cdot \frac{9}{9} - 16 = \frac{2}{3} v$

Simplify terms.

Combine $2 v$ and $\frac{9}{9}$ .

$\frac{4 v}{9} + \frac{2 v \cdot 9}{9} - 16 = \frac{2}{3} v$

Combine the numerators over the common denominator.

$\frac{4 v + 2 v \cdot 9}{9} - 16 = \frac{2}{3} v$

Simplify the numerator.

Factor $2 v$ out of $4 v + 2 v \cdot 9$ .

Factor $2 v$ out of $4 v$ .

$\frac{2 v (2) + 2 v \cdot 9}{9} - 16 = \frac{2}{3} v$

Factor $2 v$ out of $2 v \cdot 9$ .

$\frac{2 v (2) + 2 v (9)}{9} - 16 = \frac{2}{3} v$

Factor $2 v$ out of $2 v (2) + 2 v (9)$ .

$\frac{2 v (2 + 9)}{9} - 16 = \frac{2}{3} v$

Add $2$ and $9$ .

$\frac{2 v \cdot 11}{9} - 16 = \frac{2}{3} v$

Multiply $11$ by $2$ .

$\frac{22 v}{9} - 16 = \frac{2}{3} v$

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

$\frac{22 v}{9} - 16 = \frac{2 v}{3}$

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

Subtract $\frac{2 v}{3}$ from both sides of the equation.

$\frac{22 v}{9} - 16 - \frac{2 v}{3} = 0$

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

$\frac{22 v}{9} - \frac{2 v}{3} \cdot \frac{3}{3} - 16 = 0$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 v}{3}$ by $\frac{3}{3}$ .

$\frac{22 v}{9} - \frac{2 v \cdot 3}{3 \cdot 3} - 16 = 0$

Multiply $3$ by $3$ .

$\frac{22 v}{9} - \frac{2 v \cdot 3}{9} - 16 = 0$

Combine the numerators over the common denominator.

$\frac{22 v - 2 v \cdot 3}{9} - 16 = 0$

Simplify the numerator.

Factor $2 v$ out of $22 v - 2 v \cdot 3$ .

Factor $2 v$ out of $22 v$ .

$\frac{2 v (11) - 2 v \cdot 3}{9} - 16 = 0$

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

$\frac{2 v (11) + 2 v (- 1 \cdot 3)}{9} - 16 = 0$

Factor $2 v$ out of $2 v (11) + 2 v (- 1 \cdot 3)$ .

$\frac{2 v (11 - 1 \cdot 3)}{9} - 16 = 0$

Multiply $- 1$ by $3$ .

$\frac{2 v (11 - 3)}{9} - 16 = 0$

Subtract $3$ from $11$ .

$\frac{2 v \cdot 8}{9} - 16 = 0$

Multiply $8$ by $2$ .

$\frac{16 v}{9} - 16 = 0$

Add $16$ to both sides of the equation.

$\frac{16 v}{9} = 16$

Multiply both sides of the equation by $\frac{9}{16}$ .

$\frac{9}{16} \cdot \frac{16 v}{9} = \frac{9}{16} \cdot 16$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{9}{16} \cdot \frac{16 v}{9}$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{16} \cdot \frac{16 v}{9} = \frac{9}{16} \cdot 16$

Rewrite the expression.

$\frac{1}{16} (16 v) = \frac{9}{16} \cdot 16$

Cancel the common factor of $16$ .

Factor $16$ out of $16 v$ .

$\frac{1}{16} (16 (v)) = \frac{9}{16} \cdot 16$

Cancel the common factor.

$\frac{1}{16} (16 v) = \frac{9}{16} \cdot 16$

Rewrite the expression.

$v = \frac{9}{16} \cdot 16$

Simplify the right side.

Cancel the common factor of $16$ .

Cancel the common factor.

$v = \frac{9}{16} \cdot 16$

Rewrite the expression.

$v = 9$

Solve for v 8/9(1/2v-18)+2v=2/3v

Related Questions

Support LCMGCF.com by disabling your adblocker.