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

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

Step 1

Simplify $- 3 (v + 5) + 2$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 3$ by $5$ .

$- 3 v - 15 + 2 = 4 (v + 2)$

Add $- 15$ and $2$ .

$- 3 v - 13 = 4 (v + 2)$

Step 2

Simplify $4 (v + 2)$ .

Apply the distributive property.

$- 3 v - 13 = 4 v + 4 \cdot 2$

Multiply $4$ by $2$ .

$- 3 v - 13 = 4 v + 8$

Step 3

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

Subtract $4 v$ from both sides of the equation.

$- 3 v - 13 - 4 v = 8$

Subtract $4 v$ from $- 3 v$ .

$- 7 v - 13 = 8$

Step 4

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

Add $13$ to both sides of the equation.

$- 7 v = 8 + 13$

Add $8$ and $13$ .

$- 7 v = 21$

Step 5

Divide each term in $- 7 v = 21$ by $- 7$ and simplify.

Divide each term in $- 7 v = 21$ by $- 7$ .

$\frac{- 7 v}{- 7} = \frac{21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 v}{- 7} = \frac{21}{- 7}$

Divide $v$ by $1$ .

$v = \frac{21}{- 7}$

Simplify the right side.

Divide $21$ by $- 7$ .

$v = - 3$