Solve for v 5v+6=16v-3v+54

$5 v + 6 = 16 v - 3 v + 54$

Step 1

Since $v$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$16 v - 3 v + 54 = 5 v + 6$

Step 2

Subtract $3 v$ from $16 v$ .

$13 v + 54 = 5 v + 6$

Step 3

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

Subtract $5 v$ from both sides of the equation.

$13 v + 54 - 5 v = 6$

Subtract $5 v$ from $13 v$ .

$8 v + 54 = 6$

Step 4

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

Subtract $54$ from both sides of the equation.

$8 v = 6 - 54$

Subtract $54$ from $6$ .

$8 v = - 48$

Step 5

Divide each term in $8 v = - 48$ by $8$ and simplify.

Divide each term in $8 v = - 48$ by $8$ .

$\frac{8 v}{8} = \frac{- 48}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 v}{8} = \frac{- 48}{8}$

Divide $v$ by $1$ .

$v = \frac{- 48}{8}$

Simplify the right side.

Divide $- 48$ by $8$ .

$v = - 6$