Solve for v 13+2v-8+6>-7-v

$13 + 2 v - 8 + 6 > - 7 - v$

Step 1

Simplify $13 + 2 v - 8 + 6$ .

Subtract $8$ from $13$ .

$2 v + 5 + 6 > - 7 - v$

Add $5$ and $6$ .

$2 v + 11 > - 7 - v$

Step 2

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

Add $v$ to both sides of the inequality.

$2 v + 11 + v > - 7$

Add $2 v$ and $v$ .

$3 v + 11 > - 7$

Step 3

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

Subtract $11$ from both sides of the inequality.

$3 v > - 7 - 11$

Subtract $11$ from $- 7$ .

$3 v > - 18$

Step 4

Divide each term in $3 v > - 18$ by $3$ and simplify.

Divide each term in $3 v > - 18$ by $3$ .

$\frac{3 v}{3} > \frac{- 18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 v}{3} > \frac{- 18}{3}$

Divide $v$ by $1$ .

$v > \frac{- 18}{3}$

Simplify the right side.

Divide $- 18$ by $3$ .

$v > - 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$v > - 6$

Interval Notation:

$(- 6, \infty)$