Solve for v 5(2-v)-v=2(v+1)

$5 (2 - v) - v = 2 (v + 1)$

Step 1

Simplify $5 (2 - v) - v$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 2 + 5 (- v) - v = 2 (v + 1)$

Multiply $5$ by $2$ .

$10 + 5 (- v) - v = 2 (v + 1)$

Multiply $- 1$ by $5$ .

$10 - 5 v - v = 2 (v + 1)$

Subtract $v$ from $- 5 v$ .

$10 - 6 v = 2 (v + 1)$

Step 2

Simplify $2 (v + 1)$ .

Apply the distributive property.

$10 - 6 v = 2 v + 2 \cdot 1$

Multiply $2$ by $1$ .

$10 - 6 v = 2 v + 2$

Step 3

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

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

$10 - 6 v - 2 v = 2$

Subtract $2 v$ from $- 6 v$ .

$10 - 8 v = 2$

Step 4

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

Subtract $10$ from both sides of the equation.

$- 8 v = 2 - 10$

Subtract $10$ from $2$ .

$- 8 v = - 8$

Step 5

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

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $v$ by $1$ .

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

Simplify the right side.

Divide $- 8$ by $- 8$ .

$v = 1$