Solve the Inequality for v 5v+10<=-4v-17<9-2v

$5 v + 10 \leq - 4 v - 17 < 9 - 2 v$

Solve $5 v + 10 \leq - 4 v - 17$ for $v$ .

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

Add $4 v$ to both sides of the inequality.

$5 v + 10 + 4 v \leq - 17$

Add $5 v$ and $4 v$ .

$9 v + 10 \leq - 17$

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

Subtract $10$ from both sides of the inequality.

$9 v \leq - 17 - 10$

Subtract $10$ from $- 17$ .

$9 v \leq - 27$

Divide each term in $9 v \leq - 27$ by $9$ and simplify.

Divide each term in $9 v \leq - 27$ by $9$ .

$\frac{9 v}{9} \leq \frac{- 27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 v}{9} \leq \frac{- 27}{9}$

Divide $v$ by $1$ .

$v \leq \frac{- 27}{9}$

Simplify the right side.

Divide $- 27$ by $9$ .

$v \leq - 3$

Solve $- 4 v - 17 < 9 - 2 v$ for $v$ .

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

Add $2 v$ to both sides of the inequality.

$- 4 v - 17 + 2 v < 9$

Add $- 4 v$ and $2 v$ .

$- 2 v - 17 < 9$

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

Add $17$ to both sides of the inequality.

$- 2 v < 9 + 17$

Add $9$ and $17$ .

$- 2 v < 26$

Divide each term in $- 2 v < 26$ by $- 2$ and simplify.

Divide each term in $- 2 v < 26$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 v}{- 2} > \frac{26}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 v}{- 2} > \frac{26}{- 2}$

Divide $v$ by $1$ .

$v > \frac{26}{- 2}$

Simplify the right side.

Divide $26$ by $- 2$ .

$v > - 13$

Find the intersection of $v \leq - 3$ and $v > - 13$ .

$- 13 < v \leq - 3$

The result can be shown in multiple forms.

Inequality Form:

$- 13 < v \leq - 3$

Interval Notation:

$(- 13, - 3]$

Solve the Inequality for v 5v+10<=-4v-17<9-2v

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