Solve for v 3(v+2)+4=5(v-1)+v

$3 (v + 2) + 4 = 5 (v - 1) + v$

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

$5 (v - 1) + v = 3 (v + 2) + 4$

Simplify $5 (v - 1) + v$ .

Simplify each term.

Apply the distributive property.

$5 v + 5 \cdot - 1 + v = 3 (v + 2) + 4$

Multiply $5$ by $- 1$ .

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

Add $5 v$ and $v$ .

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

Simplify $3 (v + 2) + 4$ .

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $2$ .

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

Add $6$ and $4$ .

$6 v - 5 = 3 v + 10$

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

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

$6 v - 5 - 3 v = 10$

Subtract $3 v$ from $6 v$ .

$3 v - 5 = 10$

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

Add $5$ to both sides of the equation.

$3 v = 10 + 5$

Add $10$ and $5$ .

$3 v = 15$

Divide each term in $3 v = 15$ by $3$ and simplify.

Divide each term in $3 v = 15$ by $3$ .

$\frac{3 v}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 v}{3} = \frac{15}{3}$

Divide $v$ by $1$ .

$v = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$v = 5$