Solve for v 5(v+1)-v=3(v-1)+7

$5 (v + 1) - v = 3 (v - 1) + 7$

Step 1

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

Simplify each term.

Apply the distributive property.

$5 v + 5 \cdot 1 - v = 3 (v - 1) + 7$

Multiply $5$ by $1$ .

$5 v + 5 - v = 3 (v - 1) + 7$

Subtract $v$ from $5 v$ .

$4 v + 5 = 3 (v - 1) + 7$

Step 2

Simplify $3 (v - 1) + 7$ .

Simplify each term.

Apply the distributive property.

$4 v + 5 = 3 v + 3 \cdot - 1 + 7$

Multiply $3$ by $- 1$ .

$4 v + 5 = 3 v - 3 + 7$

Add $- 3$ and $7$ .

$4 v + 5 = 3 v + 4$

Step 3

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

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

$4 v + 5 - 3 v = 4$

Subtract $3 v$ from $4 v$ .

$v + 5 = 4$

Step 4

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

Subtract $5$ from both sides of the equation.

$v = 4 - 5$

Subtract $5$ from $4$ .

$v = - 1$