# How do you solve 5v + 10<= - 4v - 17< 9- 2v?

Apr 17, 2017

$- 13 < v \le - 3$

#### Explanation:

Break the inequality into 2 parts and solve each separately.

$\textcolor{b l u e}{5 v + 10 \le - 4 v - 17} < 9 - 2 v$
$5 v + 10 \le \textcolor{red}{- 4 v - 17 < 9 - 2 v}$

$\textcolor{b l u e}{5 v + 10 \le - 4 v - 17}$
$\textcolor{b l u e}{10 + 17 \le - 4 v - 5 v}$
$\textcolor{b l u e}{27 \le - 9 v} \text{ "div -9" } \leftarrow$ change sign around
$\textcolor{b l u e}{- 3 \ge v}$

$\textcolor{red}{- 4 v - 17 < 9 - 2 v}$
$\textcolor{red}{- 17 - 9 < - 2 v + 4 v}$
$\textcolor{red}{- 26 < 2 v}$
$\textcolor{red}{- 13 < v}$

Combine the two solutions for v:
$\textcolor{red}{- 13 < v} \text{ and } \textcolor{b l u e}{v \le - 3}$

$\textcolor{red}{- 13 <} v \textcolor{b l u e}{\le - 3}$