Solve for v 4(v+1)+v=3(v-2)+2

$4 (v + 1) + v = 3 (v - 2) + 2$

Step 1

Simplify $4 (v + 1) + v$ .

Simplify each term.

Apply the distributive property.

$4 v + 4 \cdot 1 + v = 3 (v - 2) + 2$

Multiply $4$ by $1$ .

$4 v + 4 + v = 3 (v - 2) + 2$

Add $4 v$ and $v$ .

$5 v + 4 = 3 (v - 2) + 2$

Step 2

Simplify $3 (v - 2) + 2$ .

Simplify each term.

Apply the distributive property.

$5 v + 4 = 3 v + 3 \cdot - 2 + 2$

Multiply $3$ by $- 2$ .

$5 v + 4 = 3 v - 6 + 2$

Add $- 6$ and $2$ .

$5 v + 4 = 3 v - 4$

Step 3

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

Subtract $3 v$ from both sides of the equation.

$5 v + 4 - 3 v = - 4$

Subtract $3 v$ from $5 v$ .

$2 v + 4 = - 4$

Step 4

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

Subtract $4$ from both sides of the equation.

$2 v = - 4 - 4$

Subtract $4$ from $- 4$ .

$2 v = - 8$

Step 5

Divide each term in $2 v = - 8$ by $2$ and simplify.

Divide each term in $2 v = - 8$ by $2$ .

$\frac{2 v}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 v}{2} = \frac{- 8}{2}$

Divide $v$ by $1$ .

$v = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$v = - 4$