Solve for v 1-5v=v+9-10v

$1 - 5 v = v + 9 - 10 v$

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.

$v + 9 - 10 v = 1 - 5 v$

Step 2

Subtract $10 v$ from $v$ .

$- 9 v + 9 = 1 - 5 v$

Step 3

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

Add $5 v$ to both sides of the equation.

$- 9 v + 9 + 5 v = 1$

Add $- 9 v$ and $5 v$ .

$- 4 v + 9 = 1$

Step 4

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

Subtract $9$ from both sides of the equation.

$- 4 v = 1 - 9$

Subtract $9$ from $1$ .

$- 4 v = - 8$

Step 5

Divide each term in $- 4 v = - 8$ by $- 4$ and simplify.

Divide each term in $- 4 v = - 8$ by $- 4$ .

$\frac{- 4 v}{- 4} = \frac{- 8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 v}{- 4} = \frac{- 8}{- 4}$

Divide $v$ by $1$ .

$v = \frac{- 8}{- 4}$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$v = 2$